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Find link is a tool written by Edward Betts.Longer titles found: Square Roots: The Story of SpongeBob SquarePants (view), Square Roots (disambiguation) (view), Methods of computing square roots (view), Conjugate (square roots) (view)

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Imaginary number
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imaginary numbers that are expressed as the principal values of the square roots of negative numbers: 6 = 36 = ( − 4 ) ( − 9 ) ≠ − 4 − 9 = ( 2 i ) ( 3Quaternion (12,273 words) [view diff] case mismatch in snippet view article find links to article

have infinitely many square roots. All others have just two (or one in the case of 0).[citation needed] Each pair of square roots of −1 creates a distinctImaginary unit (2,978 words) [view diff] case mismatch in snippet view article find links to article

square. There are two complex square roots of −1: i and − i {\displaystyle -i} , just as there are two complex square roots of every real number other thanKimbal Musk (2,167 words) [view diff] exact match in snippet view article find links to article

schoolyards across America. Musk is also the co-founder and chairman of Square Roots, an urban farming company in Brooklyn, New York City, growing food inThe Roots (6,411 words) [view diff] exact match in snippet view article find links to article

name changes that progressed through Black to the Future and then The Square Roots. Another MC, Malik B., and a permanent bass player, Leonard "Hub" HubbardIrrational number (5,469 words) [view diff] case mismatch in snippet view article find links to article

number e, the golden ratio φ, and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational. Like−1 (601 words) [view diff] case mismatch in snippet view article find links to article

algebra generalizing integers and real numbers. Although there are no real square roots of −1, the complex number i satisfies i2 = −1, and as such can be consideredMeasurement of a Circle (654 words) [view diff] case mismatch in snippet view article find links to article

root of 3 (one larger and one smaller) and other larger non-perfect square roots; however, Archimedes gives no explanation as to how he found these numbersSquare root of a matrix (4,723 words) [view diff] case mismatch in snippet view article find links to article

definite matrix § Decomposition. In general, a matrix can have several square roots. In particular, if A = B 2 {\displaystyle A=B^{2}} then A = ( − B ) 2Nested radical (3,382 words) [view diff] case mismatch in snippet view article find links to article

even when possible, it is often difficult. In the case of two nested square roots, the following theorem completely solves the problem of denesting. IfSignature matrix (231 words) [view diff] case mismatch in snippet view article find links to article

consequently a square root of the identity matrix. Note however that not all square roots of the identity are signature matrices. Noting that signature matricesExact trigonometric values (1,702 words) [view diff] case mismatch in snippet view article find links to article

angles can be expressed by a combination of arithmetic operations and square roots. The trigonometric functions of angles that are multiples of 15°, 18°Tonelli–Shanks algorithm (3,709 words) [view diff] case mismatch in snippet view article find links to article

modulo p. Tonelli–Shanks cannot be used for composite moduli: finding square roots modulo composite numbers is a computational problem equivalent to integerStraightedge and compass construction (4,702 words) [view diff] case mismatch in snippet view article find links to article

written using the four basic arithmetic operations and the extraction of square roots but of no higher-order roots. The "straightedge" and "compass" ofInvolutory matrix (893 words) [view diff] case mismatch in snippet view article find links to article

A2 = I, where I is the n × n identity matrix. Involutory matrices are all square roots of the identity matrix. This is simply a consequence of the fact thatIdentity matrix (808 words) [view diff] case mismatch in snippet view article find links to article

matrix with at least two rows and columns has an infinitude of symmetric square roots. The rank of an identity matrix I n {\displaystyle I_{n}} equals theBrāhmasphuṭasiddhānta (500 words) [view diff] case mismatch in snippet view article find links to article

manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and quadratic equations, and rules for summingReal number (5,891 words) [view diff] case mismatch in snippet view article find links to article

associated with physical reality, from imaginary numbers (such as the square roots of −1), which seemed like a theoretical contrivance unrelated to physicalRabin cryptosystem (2,419 words) [view diff] case mismatch in snippet view article find links to article

p+y_{q}\cdot q=1} . Use the Chinese remainder theorem to find the four square roots of c {\displaystyle c} modulo n {\displaystyle n} : r 1 = ( y p ⋅ p ⋅Acnode (261 words) [view diff] case mismatch in snippet view article find links to article

contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist. In fact, the complex solution set ofTheaetetus (mathematician) (370 words) [view diff] case mismatch in snippet view article

forms of irrational numbers according to the way they are expressed as square roots. This theory is presented in great detail in Book X of Euclid's ElementsShulba Sutras (3,010 words) [view diff] case mismatch in snippet view article find links to article

34}}={\frac {577}{408}}=1.4142...} Indeed, an early method for calculating square roots can be found in some Sutras[citation needed], the method involves theMulticomplex number (489 words) [view diff] case mismatch in snippet view article find links to article

Clifford numbers (elements of a Clifford algebra), since Clifford's square roots of −1 anti-commute ( i n i m + i m i n = 0 {\displaystyle i_{n}i_{m}+i_{m}i_{n}=0}Theodorus of Cyrene (934 words) [view diff] case mismatch in snippet view article find links to article

text, his student Theaetetus attributes to him the theorem that the square roots of the non-square numbers up to 17 are irrational: Theodorus here wasHierocrypt (441 words) [view diff] case mismatch in snippet view article find links to article

single 8×8-bit S-box. The key schedule uses the binary expansions of the square roots of some small integers as a source of "nothing up my sleeve numbers"Solution in radicals (364 words) [view diff] case mismatch in snippet view article find links to article

division, raising to integer powers, and the extraction of nth roots (square roots, cube roots, and other integer roots). A well-known example is the solutionCipolla's algorithm (3,026 words) [view diff] case mismatch in snippet view article find links to article

1907. Apart from prime moduli, Cipolla's algorithm is also able to take square roots modulo prime powers. Inputs: p {\displaystyle p} , an odd prime, n ∈Mathematical fallacy (3,030 words) [view diff] case mismatch in snippet view article find links to article

while squaring a number gives a unique value, there are two possible square roots of a positive number. The square root is multivalued. One value can beChi distribution (1,597 words) [view diff] case mismatch in snippet view article find links to article

chi-squared distribution by describing the distribution of the positive square roots of a variable obeying a chi-squared distribution. If Z 1 , … , Z k {\displaystyleSquare (algebra) (2,114 words) [view diff] case mismatch in snippet view article

because squares of all real numbers are non-negative. The lack of real square roots for the negative numbers can be used to expand the real number systemPrincipal value (723 words) [view diff] case mismatch in snippet view article find links to article

taking the square root of a positive real number. For example, 4 has two square roots: 2 and −2; of these the positive root, 2, is considered the principalRafael Bombelli (1,381 words) [view diff] case mismatch in snippet view article find links to article

on the topic. Bombelli avoided confusion by giving a special name to square roots of negative numbers, instead of just trying to deal with them as regularSpinor (9,857 words) [view diff] case mismatch in snippet view article find links to article

be viewed as the "square roots" of vectors (although this is inaccurate and may be misleading; they are better viewed as "square roots" of sections of vectorGraham's law (1,389 words) [view diff] case mismatch in snippet view article find links to article

rates of diffusion of different gases are inversely proportional to the square roots of their mass densities. r ∝ 1 d {\displaystyle {\mbox{r}}\propto {{\mbox{1}}Napier's bones (2,868 words) [view diff] case mismatch in snippet view article find links to article

operations and division to subtractions. Advanced use of the rods can extract square roots. Napier's bones are not the same as logarithms, with which Napier's nameNarayana Pandita (mathematician) (473 words) [view diff] case mismatch in snippet view article

mathematical developments, including a rule to calculate approximate values of square roots, investigations into the second order indeterminate equation nq2 + 1Square root of a 2 by 2 matrix (1,254 words) [view diff] case mismatch in snippet view article find links to article

many cases, such a matrix R can be obtained by an explicit formula. Square roots that are not the all-zeros matrix come in pairs: if R is a square rootMechanical computer (1,412 words) [view diff] case mismatch in snippet view article find links to article

model, the Ascota 170 accounting machine sold in the 1960s calculated square roots. Mechanical computers can be either analog, using smooth mechanisms suchLocation arithmetic (3,600 words) [view diff] case mismatch in snippet view article find links to article

not to use moves of counters on a board to multiply, divide and find square roots, but rather to find a way to compute symbolically with pen and paperSquare root of a 2 by 2 matrix (1,254 words) [view diff] case mismatch in snippet view article find links to article

many cases, such a matrix R can be obtained by an explicit formula. Square roots that are not the all-zeros matrix come in pairs: if R is a square rootRationalisation (mathematics) (938 words) [view diff] case mismatch in snippet view article

{5}})}{{\sqrt {3}}^{2}-{\sqrt {5}}^{2}}}} Now, we can proceed to remove the square roots in the denominator: 3 ( 3 − 5 ) 3 2 − 5 2 = 3 ( 3 − 5 ) 3 − 5 = 3 ( 3Quartic function (6,993 words) [view diff] case mismatch in snippet view article find links to article

obtained if one of the square roots is replaced by the symmetric one (or, what amounts to the same thing, if each of the three square roots is replaced by theGauss–Legendre algorithm (907 words) [view diff] case mismatch in snippet view article find links to article

Legendre (1752–1833) combined with modern algorithms for multiplication and square roots. It repeatedly replaces two numbers by their arithmetic and geometricComplex number (13,903 words) [view diff] case mismatch in snippet view article find links to article

equation, when all three of its roots are real numbers, contains the square roots of negative numbers, a situation that cannot be rectified by factoringMental calculation (7,242 words) [view diff] case mismatch in snippet view article find links to article

between two successive square numbers is the sum of their respective square roots. Hence, if one knows that 12 × 12 = 144 and wish to know 13 × 13, calculateAnalog multiplier (881 words) [view diff] case mismatch in snippet view article find links to article

related functions such as squares (apply same signal to both inputs), and square roots. An electronic analog multiplier can be called by several names, dependingRabdology (489 words) [view diff] case mismatch in snippet view article find links to article

technique. The rods were used to multiply, divide and even find the square roots and cube roots of numbers. The second device was a promptuary (LatinHankel singular value (294 words) [view diff] case mismatch in snippet view article find links to article

of the original model. Hankel singular values are calculated as the square roots, {σi ≥ 0, i = 1,…,n}, of the eigenvalues, {λi ≥ 0, i = 1,…,n}, for theEzra Brown (888 words) [view diff] exact match in snippet view article find links to article

Names of (7,3,1)" 2000 "Three Fermat Trails to Elliptic Curves" 1999 "Square Roots from 1; 24, 51, 10 to Dan Shanks" books 2020 (with Richard K. Guy) TheRadical symbol (880 words) [view diff] case mismatch in snippet view article find links to article

symbol is used to denote a root word. Each positive real number has two square roots, one positive and the other negative. The square root symbol refers toSingular value (1,511 words) [view diff] case mismatch in snippet view article find links to article

Hilbert spaces X {\displaystyle X} and Y {\displaystyle Y} , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operatorSlide rule (7,790 words) [view diff] case mismatch in snippet view article find links to article

More elaborate slide rules can perform other calculations, such as square roots, exponentials, logarithms, and trigonometric functions. Scales may beMental Calculation World Cup (1,569 words) [view diff] exact match in snippet view article find links to article

Myagmarsuren Tuuruul (Mongolia), 57 correct results, world cup record Square Roots from 6-digit numbers, 10 tasks in 10 minutes Winner: Naofumi OgasawaraTimeline of numerals and arithmetic (1,267 words) [view diff] case mismatch in snippet view article find links to article

understanding of indices, as well as logarithms to base 2, and computes square roots of numbers as large as a million correct to at least 11 decimal placesSubadditivity (2,790 words) [view diff] case mismatch in snippet view article find links to article

subadditive functions in various areas of mathematics, particularly norms and square roots. Additive maps are special cases of subadditive functions. A subadditiveSchizophrenic number (834 words) [view diff] case mismatch in snippet view article find links to article

value f(0) = 0. Thus, f(1) = 1, f(2) = 12, f(3) = 123, and so on. The square roots of f(n) for odd integers n give rise to a curious mixture appearing toEuclidean distance matrix (2,420 words) [view diff] case mismatch in snippet view article find links to article

the Euclidean case, squares of distances are used to avoid computing square roots and to simplify relevant theorems and algorithms. Euclidean distanceQuadratic residue (5,474 words) [view diff] case mismatch in snippet view article find links to article

roots efficiently. Say there were an efficient algorithm for finding square roots modulo a composite number. The article congruence of squares discussesQuadratic equation (6,370 words) [view diff] case mismatch in snippet view article find links to article

equating the square root of the left side with the positive and negative square roots of the right side. Solve each of the two linear equations. We illustrateKato's conjecture (211 words) [view diff] case mismatch in snippet view article find links to article

Berkeley. Kato initially posed the problem in 1953. Kato asked whether the square roots of certain elliptic operators, defined via functional calculus, are analyticPaley graph (1,552 words) [view diff] case mismatch in snippet view article find links to article

The numbers with square roots mod 13 are: ±1 (square roots ±1 for +1, ±5 for −1) ±3 (square roots ±4 for +3, ±6 for −3) ±4 (square roots ±2 for +4, ±3 forTimeline of calculus and mathematical analysis (1,539 words) [view diff] exact match in snippet view article find links to article

University. Retrieved 2022-11-03. "On Squares, Rectangles, and Square Roots - Square roots in ancient Chinese mathematics | Mathematical Association ofViète's formula (2,256 words) [view diff] case mismatch in snippet view article find links to article

involves nested square roots of two, but uses only one multiplication: π = lim k → ∞ 2 k 2 − 2 + 2 + 2 + 2 + ⋯ + 2 ⏟ k square roots , {\displaystyleGlaeser's continuity theorem (156 words) [view diff] case mismatch in snippet view article find links to article

theorem is a characterization of the continuity of the derivative of the square roots of functions of class C 2 {\displaystyle C^{2}} . It was introduced inThe Roots discography (913 words) [view diff] exact match in snippet view article find links to article

plays, and two live albums. The Roots began performing in 1989 as The Square Roots with rapper Black Thought and drummer Questlove. Rapper Malik B., andCholesky decomposition (7,128 words) [view diff] case mismatch in snippet view article find links to article

and used with essentially the same algorithms, but avoids extracting square roots. For this reason, the LDL decomposition is often called the square-root-freeKhinchin's constant (1,457 words) [view diff] case mismatch in snippet view article find links to article

roots of quadratic equations (including the golden ratio Φ and the square roots of integers), and the base of the natural logarithm e. Khinchin is sometimesDivine Proportions: Rational Trigonometry to Universal Geometry (1,478 words) [view diff] case mismatch in snippet view article find links to article

coordinates, and can be calculated directly without the need for the square roots needed to calculate distances from coordinates or the inverse trigonometricWahba's problem (629 words) [view diff] no match in snippet view article find links to article

Orthogonal Procrustes problem (consider all the vectors multiplied by the square-roots of the corresponding weights as columns of two matrices with N columnsBerlekamp–Rabin algorithm (1,985 words) [view diff] case mismatch in snippet view article find links to article

Rabin. In 1986 René Peralta proposed a similar algorithm for finding square roots in Z p {\displaystyle \mathbb {Z} _{p}} . In 2000 Peralta's method wasRoot of unity (5,700 words) [view diff] case mismatch in snippet view article find links to article

proved that a primitive nth root of unity can be expressed using only square roots, addition, subtraction, multiplication and division if and only if itSunday (2011 film) (462 words) [view diff] exact match in snippet view article

Montreal. Doyon had previously created a three-minute animated short Square Roots in 2006, while enrolled in the NFB's Hothouse program for young animatorsMiller–Rabin primality test (4,975 words) [view diff] case mismatch in snippet view article find links to article

probable prime to base a, on which the Fermat test is based); the only square roots of 1 modulo n are 1 and −1. Hence, by contraposition, if n is not a strongRounding (7,477 words) [view diff] case mismatch in snippet view article find links to article

fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating-point representationTimeline of algebra (1,217 words) [view diff] case mismatch in snippet view article find links to article

century AD Hero of Alexandria gives the earliest fleeting reference to square roots of negative numbers. c. 150 Greek mathematician Hero of Alexandria, treatsEstienne de La Roche (230 words) [view diff] case mismatch in snippet view article find links to article

excellent handbook of algebra using an elegant notation for powers, square roots and roots of a higher nature. However, in 1880, Aristide Marre publishedQuintic function (4,142 words) [view diff] case mismatch in snippet view article find links to article

four different square roots for writing all the roots of a solvable quintic. Even for the first root that involves at most two square roots, the expressionMichele Cipolla (169 words) [view diff] case mismatch in snippet view article find links to article

things) a theory for sequences of sets and Cipolla's algorithm for finding square roots modulo a prime number. He also solved the problem of binomial congruenceNumber (7,738 words) [view diff] case mismatch in snippet view article find links to article

vanishing points in perspective drawing. The earliest fleeting reference to square roots of negative numbers occurred in the work of the mathematician and inventorSHA-2 (4,382 words) [view diff] case mismatch in snippet view article find links to article

Initialize hash values: (first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19): h0 := 0x6a09e667 h1 := 0xbb67ae85 h2 :=Bijaganita (251 words) [view diff] case mismatch in snippet view article find links to article

Bijaganita is the first text to recognize that a positive number has two square roots The translations or editions of the Bijaganita into English include:Timeline of mathematics (7,394 words) [view diff] case mismatch in snippet view article find links to article

Greece, Heron of Alexandria, (Hero) the earliest fleeting reference to square roots of negative numbers. c 100 – Greece, Theon of Smyrna 60 – 120 – GreeceBrahmagupta (5,870 words) [view diff] case mismatch in snippet view article find links to article

integer and later gives rules facilitating the computation of squares and square roots. He then gives rules for dealing with five types of combinations of fractions:Circle Limit III (1,158 words) [view diff] case mismatch in snippet view article find links to article

obtained by calculations in the field of rational numbers extended by the square roots of two and three. Viewed as a pattern, ignoring the colors of the fishHilbert's fifth problem (1,049 words) [view diff] case mismatch in snippet view article find links to article

Smirnov. Ark. Mat. 8, 107–109. Enflo, P. (1970). "Uniform structures and square roots in topological groups". Israel Journal of Mathematics. 8 (3): 230–252Quadratic integer (2,660 words) [view diff] case mismatch in snippet view article find links to article

called rational integers. Common examples of quadratic integers are the square roots of rational integers, such as √2, and the complex number i = √–1, whichDistance set (970 words) [view diff] case mismatch in snippet view article find links to article

the distance set of the two-dimensional integer lattice: they are the square roots of integers whose prime factorization does not contain an odd numberHamiltonian matrix (647 words) [view diff] case mismatch in snippet view article find links to article

in this basis is Hamiltonian. Ikramov, Khakim D. (2001), "Hamiltonian square roots of skew-Hamiltonian matrices revisited", Linear Algebra and its ApplicationsOperation (mathematics) (1,186 words) [view diff] case mismatch in snippet view article

For example, in the real numbers one cannot divide by zero or take square roots of negative numbers. The values for which an operation is defined form2 (2,002 words) [view diff] case mismatch in snippet view article find links to article

normally be written for cubic and other roots, may simply be left blank for square roots, as it is tacitly understood. The square root of 2 was the first knownJan van Koningsveld (195 words) [view diff] exact match in snippet view article find links to article

1969 in Emden) is a mental calculator. He is the champion of Extracting Square Roots of 2004 and 2008 as well as the champion of Calendar Calculation of 2008Juan de Ortega (mathematician) (409 words) [view diff] case mismatch in snippet view article

commercial arithmetic, and discovered an improved method for calculating square roots. Very little is known of Ortega's life. He was a member of the Dominican257-gon (577 words) [view diff] case mismatch in snippet view article find links to article

numbers, and like all constructible numbers they can be written using square roots and no higher-order roots. Although it was known to Gauss by 1801 thatMatrix decomposition (3,470 words) [view diff] case mismatch in snippet view article find links to article

An alternative is the LDL decomposition, which can avoid extracting square roots. Applicable to: m-by-n matrix A with linearly independent columns Decomposition:15 (number) (1,312 words) [view diff] case mismatch in snippet view article

compass and unmarked straightedge, and cos π/15 is expressible in terms of square roots. There are 15 monohedral convex pentagonal tilings, with 8 being edge-to-edgeNumerical linear algebra (2,500 words) [view diff] case mismatch in snippet view article find links to article

are called the singular values of A. Because singular values are the square roots of the eigenvalues of A A ∗ {\displaystyle AA^{\ast }} , there is a tightImmanuel Bonfils (627 words) [view diff] case mismatch in snippet view article find links to article

the diameter and circumference of a circle and methods of calculating square roots. Bonfils, Immanuel (1365), The Wings of Eagles, Hebrew: שש כנפים, inBlack Thought (2,611 words) [view diff] exact match in snippet view article find links to article

Trotter subsequently spent some time as one of two MCs in the group the Square Roots; the other was Malik B., whom Tariq met in college. In high school, BlackFour fours (2,131 words) [view diff] case mismatch in snippet view article find links to article

integer. This works by noticing three things: 1) It is possible to take square roots repeatedly without using any additional 4s 2) A square root can also51 (number) (611 words) [view diff] case mismatch in snippet view article

is constructible, and the number cos π/51 is expressible in terms of square roots. 51 is: The atomic number of antimony The code for international directArs Magna (Cardano book) (784 words) [view diff] case mismatch in snippet view article

numbers (chapter XXXVII). The problem mentioned by Cardano which leads to square roots of negative numbers is: find two numbers whose sum is equal to 10 andSum of radicals (524 words) [view diff] case mismatch in snippet view article find links to article

coordinates may be expressed using the Pythagorean theorem as a sum of integer square roots, so in order to determine whether one path is longer or shorter thanBlum integer (396 words) [view diff] case mismatch in snippet view article find links to article

quadratic residues modulo n and coprime to n and a ∈ Qn. Then: a has four square roots modulo n, exactly one of which is also in Qn The unique square root ofMultivalued function (1,788 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle f(z)} . Every real number greater than zero has two real square roots, so that square root may be considered a multivalued function. For exampleStandard deviation (7,569 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \textstyle (x_{1}-{\bar {x}},\;\dots ,\;x_{n}-{\bar {x}}).} Taking square roots reintroduces bias (because the square root is a nonlinear function whichComplex plane (4,512 words) [view diff] case mismatch in snippet view article find links to article

the resulting value must be restricted somehow. When dealing with the square roots of non-negative real numbers this is easily done. For instance, we canStandard algorithms (411 words) [view diff] case mismatch in snippet view article find links to article

calculators has made manual calculation less important (see the note on square roots, above) and cursory teaching of traditional methods has created failureChinese multiplication table (854 words) [view diff] case mismatch in snippet view article find links to article

calculus for carrying out multiplication, division, the extraction of square roots, and the solving of equations based on place value decimal notation.Function (mathematics) (10,867 words) [view diff] case mismatch in snippet view article

through the computation of the zeros of auxiliary functions. Similarly, if square roots occur in the definition of a function from R {\displaystyle \mathbb {R}Spiral of Theodorus (1,170 words) [view diff] case mismatch in snippet view article find links to article

of his work. It is assumed that Theodorus had proved that all of the square roots of non-square integers from 3 to 17 are irrational by means of the SpiralCaamp (460 words) [view diff] exact match in snippet view article find links to article

four albums. Their first album, self-titled, was released in 2016 on Square Roots Records. In 2018, Caamp released a six-song EP. Their second album, ByWilbur Knorr (926 words) [view diff] case mismatch in snippet view article find links to article

the square roots of the integers up to 17, and Theodorus' student Theaetetus, who showed that all non-square integers have irrational square roots. KnorrIsaac ben Moses Eli (166 words) [view diff] case mismatch in snippet view article find links to article

of numbers, dealing with the first four rules and the extraction of square roots; (2) proportion, etc.; and (3) elementary geometry. The book is an introductionRabin signature algorithm (1,893 words) [view diff] case mismatch in snippet view article find links to article

computing square roots modulo a prime—picking p ≡ q ≡ 3 ( mod 4 ) {\displaystyle p\equiv q\equiv 3{\pmod {4}}} makes it easiest. Square roots are not uniqueSHA-1 (5,544 words) [view diff] case mismatch in snippet view article find links to article

nothing up my sleeve numbers: The four round constants k are 230 times the square roots of 2, 3, 5 and 10. However they were incorrectly rounded to the nearest65537-gon (569 words) [view diff] case mismatch in snippet view article find links to article

and like any constructible numbers, they can be written in terms of square roots and no higher-order roots. Although it was known to Gauss by 1801 thatGalois theory (4,048 words) [view diff] case mismatch in snippet view article find links to article

subtraction, multiplication, division) and application of radicals (square roots, cube roots, etc)? The Abel–Ruffini theorem provides a counterexampleMathematical constant (3,533 words) [view diff] case mismatch in snippet view article find links to article

square. There are in fact two complex square roots of −1, namely i and −i, just as there are two complex square roots of every other real number (exceptIndian mathematics (13,468 words) [view diff] case mismatch in snippet view article find links to article

solutions to the examples. The topics treated include arithmetic (fractions, square roots, profit and loss, simple interest, the rule of three, and regula falsi)Hippocrates of Chios (732 words) [view diff] exact match in snippet view article find links to article

Quadrature of the Circle and Hippocrates' Lunes at Convergence Mesolabe Compass and Square Roots - Numberphile video explaining Hippocrates' mesolabe compassPin group (1,982 words) [view diff] case mismatch in snippet view article find links to article

situation is as follows. The Clifford algebra generated by 3 anticommuting square roots of +1 is the algebra of 2×2 complex matrices, and Pin+(3) is isomorphicNothing-up-my-sleeve number (1,315 words) [view diff] case mismatch in snippet view article find links to article

the square roots of small integers to produce the constants used in its "Secure Hash Algorithm" SHA-1. The SHA-2 functions use the square roots and cubeLucas pseudoprime (3,646 words) [view diff] case mismatch in snippet view article find links to article

limit. Perfect squares are easy to detect using Newton's method for square roots. We choose a Lucas sequence where the Jacobi symbol ( D n ) = − 1 {\displaystyleBiquaternion (3,161 words) [view diff] case mismatch in snippet view article find links to article

+w\mathbf {j} +x\mathbf {k} } is a biquaternion.: 639 To distinguish square roots of minus one in the biquaternions, Hamilton: 730 and Arthur W. ConwayJohnny Ball (1,849 words) [view diff] exact match in snippet view article find links to article

episodes he spoke about "Russian multiplication", "The Mesolabe Compass and Square Roots", "Parabolas and Archimedes", "The Volume of a Sphere", and "Area ofEuclid's Elements (5,051 words) [view diff] case mismatch in snippet view article find links to article

irrationality of the square roots of non-square integers (e.g. 2 {\displaystyle {\sqrt {2}}} ) and classifies the square roots of incommensurable linesVery smooth hash (1,989 words) [view diff] case mismatch in snippet view article find links to article

version of Very Smooth Hash function, this hard problem is to find modular square roots (VSSR) of certain special numbers (VSN). This is assumed to be as hardPre-algebra (444 words) [view diff] case mismatch in snippet view article find links to article

in scientific notation is 3.4 × 108) Identifying Probability Solving Square roots Pythagorean Theorem Pre-algebra may include subjects from geometry, especiallyAlgebraic number (1,501 words) [view diff] case mismatch in snippet view article find links to article

from these using the basic arithmetic operations and the extraction of square roots. (By designating cardinal directions for 1, −1, i, and −i, complex numbersInequation (752 words) [view diff] case mismatch in snippet view article find links to article

programming. Usually because of the properties of certain functions (like square roots), some inequations are equivalent to a combination of multiple othersSquare One (band) (699 words) [view diff] exact match in snippet view article

Caribbean Music Awards at the Harlem Apollo in 1993. After a further album, Square Roots, they parted ways with Ice Records in 1995. Their next album 4 SidesTrigonometric functions (8,638 words) [view diff] case mismatch in snippet view article find links to article

}={\frac {\sqrt {4}}{2}}=1} (right angle) Writing the numerators as square roots of consecutive non-negative integers, with a denominator of 2, providesUltraSPARC (492 words) [view diff] no match in snippet view article find links to article

executes floating point adds and subtracts, one multiplies, one divides and square-roots. Two units are for executing SIMD instructions defined by the VisualComputer (13,366 words) [view diff] case mismatch in snippet view article find links to article

development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithmsPell number (3,664 words) [view diff] case mismatch in snippet view article find links to article

the square of P2 + P3 = 2 + 5 = 7. The numbers P2n + P2n+1 forming the square roots of these sums, 1, 7, 41, 239, 1393, 8119, 47321,… (sequence A002315 inPseudo-Euclidean space (2,336 words) [view diff] case mismatch in snippet view article find links to article

the vector norm (and distance) in an invariant manner, one has to get square roots of scalar squares, which leads to possibly imaginary distances; see squareQuadratic irrational number (1,618 words) [view diff] case mismatch in snippet view article find links to article

proved irrational. Theodorus of Cyrene proved the irrationality of the square roots of non-square natural numbers up to 17, but stopped there, probably becausePeter Barlow (mathematician) (695 words) [view diff] case mismatch in snippet view article

The latter became known as Barlow's Tables and gives squares, cubes, square roots, cube roots, and reciprocals of all integer numbers from 1 to 10,000Euclidean distance (2,945 words) [view diff] exact match in snippet view article find links to article

JSTOR 2959270, MR 0365798 Moler, Cleve and Donald Morrison (1983), "Replacing Square Roots by Pythagorean Sums" (PDF), IBM Journal of Research and Development,Probable prime (1,070 words) [view diff] case mismatch in snippet view article find links to article

25·109.: 1005 This test may be improved by using the fact that the only square roots of 1 modulo a prime are 1 and −1. Write n = d · 2s + 1, where d is oddWhere's Willy? (521 words) [view diff] case mismatch in snippet view article find links to article

[1-({\rm {days\ of\ inactivity}}/100)]} Because of the nature of square roots and natural logarithms, the higher a user's bills entered and hits areStrong pseudoprime (1,336 words) [view diff] case mismatch in snippet view article find links to article

(it equals 29×1093). Modulo a prime, the residue 1 can have no other square roots than 1 and minus 1. This shows that 31697 is not a strong pseudoprimeGeometric mean theorem (1,234 words) [view diff] case mismatch in snippet view article find links to article

area of the rectangle. The method also allows for the construction of square roots (see constructible number), since starting with a rectangle that hasInverse hyperbolic functions (4,311 words) [view diff] case mismatch in snippet view article find links to article

except for non-positive real values of the variables (where the two square roots have a zero real part). This principal value of the square root functionRai Sahib (786 words) [view diff] exact match in snippet view article find links to article

Examination of Sir Isaac Newton's Rule for finding the Number of Imaginary Square Roots in an Equation". Dukhan Ram – Indian ophthalmologist, legislator andMoseley's law (1,173 words) [view diff] case mismatch in snippet view article find links to article

}} lines. Moseley derived his formula empirically by line fitting the square roots of the X-ray frequencies plotted by atomic number, and his formula couldHolstein–Primakoff transformation (1,284 words) [view diff] case mismatch in snippet view article find links to article

transformation is particularly useful in the case where s is large, when the square roots can be expanded as Taylor series, to give an expansion in decreasingYang Hui (680 words) [view diff] case mismatch in snippet view article find links to article

(詳解九章算法) of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's Triangle" was invented by mathematicianWPrime (243 words) [view diff] case mismatch in snippet view article find links to article

WPrime is a computer program that calculates a set number of square roots using Newton's method for estimating functions verifying the results by squaringCasus irreducibilis (3,364 words) [view diff] case mismatch in snippet view article find links to article

understanding of the time: cube roots from non-real numbers, i.e. from square roots from negative numbers) to express them in radicals, this case in theDivision polynomials (1,177 words) [view diff] exact match in snippet view article find links to article

link] Schoof: Elliptic Curves over Finite Fields and the Computation of Square Roots mod p. Math. Comp., 44(170):483–494, 1985. Available at http://www.matHistory of manifolds and varieties (1,432 words) [view diff] case mismatch in snippet view article find links to article

of research. The standard forms for elliptic integrals involved the square roots of cubic and quartic polynomials. When those were replaced by polynomialsNon-standard model of arithmetic (1,162 words) [view diff] case mismatch in snippet view article find links to article

is larger than m ⋅ u for any standard finite m. Also one can define "square roots" such as the least v such that v2 > 2 ⋅ u. These cannot be within a standard1616 in science (399 words) [view diff] case mismatch in snippet view article find links to article

efficient method of finding logarithms by the continued extraction of square roots. Croatian mathematician Fausto Veranzio publishes Machinae novae, a bookDinanath Atmaram Dalvi (608 words) [view diff] exact match in snippet view article find links to article

Examination of Sir Isaac Newton's Rule for finding the Number of Imaginary Square Roots in an Equation". He was Examiner for first Examination in Arts, AnalyticImage (mathematics) (2,288 words) [view diff] case mismatch in snippet view article

{\displaystyle f} is the empty set, because the negative numbers do not have square roots in the set of reals. f : R 2 → R {\displaystyle f:\mathbb {R} ^{2}\toBc (programming language) (1,652 words) [view diff] case mismatch in snippet view article

: are not available in POSIX bc. The sqrt() function for calculating square roots is POSIX bc's only built-in mathematical function. Other functions areClosed-form expression (1,419 words) [view diff] case mismatch in snippet view article find links to article

(third and fourth degree) equations can be expressed using arithmetic, square roots, and nth roots. However, there are quintic equations without such closed-formProof of impossibility (4,023 words) [view diff] case mismatch in snippet view article find links to article

and solids ... — Heath,[citation needed] Proofs followed for various square roots of the primes up to 17. There is a famous passage in Plato's TheaetetusPhysics beyond the Standard Model (5,011 words) [view diff] case mismatch in snippet view article find links to article

matrix in a 3-dimensional vector space, "rotates" a vector composed of square roots of down-type quark masses ( m d , m s , m b ) {\displaystyle ({\sqrtPPP (complexity) (1,000 words) [view diff] case mismatch in snippet view article

Retrieved 2009-12-11. Emil Jeřábek (2016). "Integer factoring and modular square roots". Journal of Computer and System Sciences. 82 (2): 380–394. arXiv:1207Science and technology of the Han dynasty (14,228 words) [view diff] case mismatch in snippet view article find links to article

Han-era Chinese advancements in mathematics include the discovery of square roots, cube roots, the Pythagorean theorem, Gaussian elimination, the HornerEgyptian geometry (1,492 words) [view diff] case mismatch in snippet view article find links to article

interesting because it is clear that the Egyptians were familiar with square roots. They even had a special hieroglyph for finding a square root. It looksEffusion (1,271 words) [view diff] case mismatch in snippet view article find links to article

the same temperature and pressure is given by the inverse ratio of the square roots of the masses of the gas particles. Rate of effusion of gas 1 Rate ofLegendre's conjecture (770 words) [view diff] case mismatch in snippet view article find links to article

difference between two consecutive squares is of the order of their square roots. Stewart, Ian (2013), Visions of Infinity: The Great Mathematical ProblemsMTV (Philippine TV channel) (1,378 words) [view diff] exact match in snippet view article

Paris Hilton's My New BFF The Playlist Roll Out Spanking New Sessions Square Roots: The Story of SpongeBob SquarePants Teen Cribs Tong Hits World StageQuadratic reciprocity (8,522 words) [view diff] case mismatch in snippet view article find links to article

{4}}} using Euler's criterion one can give an explicit formula for the "square roots" modulo p {\displaystyle p} of a quadratic residue a {\displaystyle a}Algebra (5,612 words) [view diff] case mismatch in snippet view article find links to article

Σn2, Σn3 and used the method of successive approximation to determine square roots. François Viète's work on new algebra at the close of the 16th centuryShor's algorithm (6,489 words) [view diff] case mismatch in snippet view article find links to article

four distinct square roots of 1 {\displaystyle 1} modulo N {\displaystyle N} , and therefore at least two distinct non-trivial square roots exist. In factHeptadecagon (1,537 words) [view diff] case mismatch in snippet view article find links to article

finding the cosine of 2 π / 17 {\displaystyle 2\pi /17} in terms of square roots. Gauss's book Disquisitiones Arithmeticae gives this (in modern notation)Book on Numbers and Computation (802 words) [view diff] case mismatch in snippet view article find links to article

position method for finding roots and the extraction of approximate square roots; calculation of the volume of various 3-dimensional shapes; relativeArcade video game (8,761 words) [view diff] exact match in snippet view article find links to article

throughout the 1980s and beyond. Bienaimé, Pierre (13 January 2012). "Square Roots: Donkey Kong (NES)". Nintendojo. Archived from the original on 1 FebruaryKoide formula (1,944 words) [view diff] case mismatch in snippet view article find links to article

and tau, 1/3 ≤ Q < 1 . The upper bound follows from the fact that the square roots are necessarily positive, and the lower bound follows from theMin-max theorem (2,721 words) [view diff] case mismatch in snippet view article find links to article

maximum eigenvalue. The singular values {σk} of a square matrix M are the square roots of the eigenvalues of M*M (equivalently MM*). An immediate consequence[citationCongruence of squares (644 words) [view diff] case mismatch in snippet view article find links to article

factorization, and Dixon's factorization. Conversely, because finding square roots modulo a composite number turns out to be probabilistic polynomial-timeCorrespondence analysis (3,307 words) [view diff] case mismatch in snippet view article find links to article

{w_{m}}}} respectively i.e. the vector elements are the inverses of the square roots of the masses. The off-diagonal elements are all 0. Next, compute matrixLiu Hui's π algorithm (2,704 words) [view diff] case mismatch in snippet view article find links to article

requiring only one addition and one square root extraction. Calculation of square roots of irrational numbers was not an easy task in the third century withAl-Mahani (1,206 words) [view diff] case mismatch in snippet view article find links to article

as well as square and cubic roots as irrational magnitudes. He called square roots "plane irrationalities" and cubic roots "solid irrationalities", andSquare triangular number (1,683 words) [view diff] case mismatch in snippet view article find links to article

172 − 1 = 2 × 122, and 1681 = 412 = 2 × 292 − 1. In each case, the two square roots involved multiply to give sk: 5 × 7 = 35, 12 × 17 = 204, and 29 × 41Square root of 3 (941 words) [view diff] case mismatch in snippet view article find links to article

url-status (link) S., D.; Jones, M. F. (1968). "22900D approximations to the square roots of the primes less than 100". Mathematics of Computation. 22 (101): 234–235Quadratic sieve (4,638 words) [view diff] case mismatch in snippet view article find links to article

We are now left with the equality a2 = b2 mod n from which we get two square roots of (a2 mod n), one by taking the square root in the integers of b2 namelyRegular polygon (3,220 words) [view diff] case mismatch in snippet view article find links to article

terms of the four basic arithmetic operations and the extraction of square roots. A regular skew polygon in 3-space can be seen as nonplanar paths zig-zaggingJacques Tilouine (330 words) [view diff] case mismatch in snippet view article find links to article

groups. Harris, Michael; Tilouine, Jacques (2001). "p-adic measures and square roots of special values of triple product L-functions". Mathematische AnnalenHP calculators (582 words) [view diff] case mismatch in snippet view article find links to article

floating-point numbers, trigonometric functions, logarithms, exponentiation, and square roots. This new calculator was well received by the customer base, but WilliamType (model theory) (2,240 words) [view diff] case mismatch in snippet view article

over the rationals with leading coefficient 1. For example, the type of square roots of 2. Each of these types is an open point of the Stone space. TranscendentalFinger-counting (2,128 words) [view diff] case mismatch in snippet view article find links to article

performing complex operations, including the approximate determination of square roots. Several pedagogical poems dealt exclusively with finger counting, someOrdered field (1,792 words) [view diff] case mismatch in snippet view article find links to article

of Liège. Retrieved 2013-05-04. Lam (2005) p. 236 The squares of the square roots √−7 and √1−p are in Q, but are <0, so that these roots cannot be in QIbn al-Banna' al-Marrakushi (845 words) [view diff] case mismatch in snippet view article find links to article

the Workings of Calculations) which covered topics such as computing square roots of a number and the theory of continued fractions. List of Arab scientistsConstructible polygon (2,121 words) [view diff] case mismatch in snippet view article find links to article

terms of the four basic arithmetic operations and the extraction of square roots. Equivalently, a regular n-gon is constructible if any root of the nthOblivious transfer (1,987 words) [view diff] case mismatch in snippet view article find links to article

N) = 1 with overwhelming probability, which ensures that there are 4 square roots of x2 mod N. The sender finds a square root y of x2 mod N and sends yTetration (6,413 words) [view diff] case mismatch in snippet view article find links to article

{\sqrt[{y}]{x}}=\log _{y}x} Like square roots, the square super-root of x may not have a single solution. Unlike square roots, determining the number of squareCalculator (7,939 words) [view diff] case mismatch in snippet view article find links to article

(ROM) The instructions for in-built functions (arithmetic operations, square roots, percentages, trigonometry, etc.) are stored here in binary form. TheseSquare Enix Europe (4,228 words) [view diff] exact match in snippet view article find links to article

CEO". square-enix-games.com. Retrieved 15 August 2020. Weber, Rachel. "Square Roots: The man in charge of Square Enix's Western future". GamesIndustry.bizDonald in Mathmagic Land (1,338 words) [view diff] case mismatch in snippet view article find links to article

Mathmagic Land. This "mighty strange" fantasy land contains trees with square roots, a stream flowing with numbers, and a walking pencil that plays tic-tac-toeBiquadratic field (287 words) [view diff] case mismatch in snippet view article find links to article

Klein four-group. Biquadratic fields are all obtained by adjoining two square roots. Therefore in explicit terms they have the form K = Q(√a,√b) for rationalCayley–Purser algorithm (1,139 words) [view diff] case mismatch in snippet view article find links to article

\gamma } is computationally infeasible, at least as hard as finding square roots mod n (see quadratic residue). It could be recovered from α {\displaystyleFermat's little theorem (2,323 words) [view diff] case mismatch in snippet view article find links to article

integers modulo p form a finite field, in which 1 modulo p has exactly two square roots, 1 and −1 modulo p. Note that ad ≡ 1 (mod p) holds trivially for a ≡List of FoxTrot books (122 words) [view diff] exact match in snippet view article find links to article

(minus week of July 23–28, 2001) ISBN 0-7407-2191-7 Your Momma Thinks Square Roots Are Vegetables April 11, 2003 August 26, 2001 – April 14, 2002 (plusQuestlove (2,895 words) [view diff] exact match in snippet view article find links to article

Performing Arts. By the time he graduated, he had founded a band called the Square Roots (later dropping the word "square") with his friend Tariq Trotter (BlackRotation matrix (14,569 words) [view diff] case mismatch in snippet view article find links to article

diagonal. We can, in fact, obtain all four magnitudes using sums and square roots, and choose consistent signs using the skew-symmetric part of the off-diagonalLiber Abaci (1,857 words) [view diff] case mismatch in snippet view article find links to article

approximations, both numerical and geometrical, of irrational numbers such as square roots. The book also includes proofs in Euclidean geometry. Fibonacci's methodTimeline of algorithms (1,911 words) [view diff] case mismatch in snippet view article find links to article

Babylonians develop earliest known algorithms for factorization and finding square roots c. 300 BC – Euclid's algorithm c. 200 BC – the Sieve of Eratosthenes4,294,967,295 (798 words) [view diff] case mismatch in snippet view article find links to article

2 π / n ) {\displaystyle \cos(2\pi /n)} can be expressed in terms of square roots. Not only is 4,294,967,295 the largest known odd number of sides of aSingular value decomposition (11,319 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \mathbf {\Sigma } } (non-zero singular values) are the square roots of the non-zero eigenvalues of M⁎M or MM⁎. In the special case that MPolynomial (8,018 words) [view diff] case mismatch in snippet view article find links to article

the 16th century, similar formulas (using cube roots in addition to square roots), although much more complicated, are known for equations of degree threeCasio fx-7000G (830 words) [view diff] case mismatch in snippet view article find links to article

the calculator include arithmetic and algebraic computations such as: square roots reciprocals exponential functions factorials logarithms trig functionsMahalanobis distance (2,555 words) [view diff] case mismatch in snippet view article find links to article

is positive-definite, so is S − 1 {\displaystyle S^{-1}} , thus the square roots are always defined. We can find useful decompositions of the squaredSrinivasa Ramanujan (10,825 words) [view diff] case mismatch in snippet view article find links to article

7 (4): 131–133. Ramanujan, S. (1915). "Short Note: On the sum of the square roots of the first n natural numbers". The Journal of the Indian MathematicalRandomized algorithm (3,633 words) [view diff] case mismatch in snippet view article find links to article

can be traced back to Pocklington's algorithm, from 1917, which finds square roots modulo prime numbers. The study of randomized algorithms in number theoryCasio fx-7000G (830 words) [view diff] case mismatch in snippet view article find links to article

the calculator include arithmetic and algebraic computations such as: square roots reciprocals exponential functions factorials logarithms trig functionsSinclair Oxford (336 words) [view diff] case mismatch in snippet view article find links to article

introduced in 1975 introducing the ability to calculate percentages and square roots. The Oxford 200 included memory and sold for £19.95. The Oxford 300 wasPoint of View (Cassandra Wilson album) (332 words) [view diff] exact match in snippet view article

described Wilson as a "chance-taking singer in a funky M-Base setting." "Square Roots" (Cassandra Wilson) – 4:39 "Blue in Green" (Miles Davis, Bill Evans,Pulse shaping (994 words) [view diff] case mismatch in snippet view article find links to article

receiver filters. The filters' amplitude responses are thus pointwise square roots of the system filters. Other approaches that eliminate complex pulseYuktibhāṣā (2,023 words) [view diff] case mismatch in snippet view article find links to article

contain elementary mathematics, such as division, the Pythagorean theorem, square roots, etc. Novel ideas are not discussed until the sixth chapter on circumferenceDaniel Shanks (748 words) [view diff] case mismatch in snippet view article find links to article

Fermat's factorization method; and the Tonelli–Shanks algorithm that finds square roots modulo a prime, which is useful for the quadratic sieve method of integerFermat's factorization method (1,402 words) [view diff] no match in snippet view article find links to article

{\displaystyle b^{2}} are squares: It is not necessary to compute all the square-roots of a 2 − N {\displaystyle a^{2}-N} , nor even examine all the valuesEunuch (9,565 words) [view diff] case mismatch in snippet view article find links to article

mathematician; invented the Jia Xian triangle for the calculation of square roots and cube roots. Ly Thuong Kiet (1019–1105): general during the Lý DynastyPPA (complexity) (557 words) [view diff] exact match in snippet view article

authors parameter (link) E. Jeřábek (2016). "Integer Factoring and Modular Square Roots". Journal of Computer and System Sciences. 82 (2): 380–394. arXiv:1207Polykleitos (2,064 words) [view diff] case mismatch in snippet view article find links to article

human male body.: 309 The process would not require measurement of square roots: the artist could take a long cord and make knots separated from eachLemaître coordinates (774 words) [view diff] no match in snippet view article find links to article

(the numerator and denominator are switched inside the square-roots), leads to the Lemaître coordinate expression of the metric, d s 2 =Jacobi eigenvalue algorithm (3,529 words) [view diff] case mismatch in snippet view article find links to article

Singular values The singular values of a (square) matrix A are the square roots of the (non-negative) eigenvalues of A T A {\displaystyle A^{T}A} . InSunzi Suanjing (516 words) [view diff] case mismatch in snippet view article find links to article

of fractions, followed by mechanical algorithm for the extraction of square roots. Chapter 3 contains the earliest example of Chinese remainder theoremHistory of mathematics (15,392 words) [view diff] case mismatch in snippet view article find links to article

the first to recognize the possibility of negative numbers possessing square roots. Menelaus of Alexandria (c. 100 AD) pioneered spherical trigonometryElliptic geometry (2,736 words) [view diff] case mismatch in snippet view article find links to article

algebra of William Rowan Hamilton: he envisioned a sphere as a domain of square roots of minus one. Then Euler's formula exp ( θ r ) = cos θ + r sin Noureen DeWulf (697 words) [view diff] exact match in snippet view article find links to article

13 episodes 2015–2016 Grandfathered Priya Guest role; 2 episodes 2016 Square Roots Saleena Desai Television film 2016 Hell's Kitchen Herself Episode: "CrepeMandelbrot set (6,638 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle z\mapsto z^{3}+3kz+c} , whose two critical points are the complex square roots of the parameter k. A parameter is in the cubic connectedness locus ifCounting rods (1,906 words) [view diff] case mismatch in snippet view article find links to article

wide range of calculations, including finding the value of π, finding square roots, cube roots, or higher order roots, and solving a system of linear equationsList of numbers (3,853 words) [view diff] exact match in snippet view article find links to article

Lipscombe, Trevor Davis (2021-05-06), "Super Powers: Calculate Squares, Square Roots, Cube Roots, and More", Quick(er) Calculations, Oxford University PressAnalytical Engine (3,620 words) [view diff] case mismatch in snippet view article find links to article

perform all four arithmetic operations, plus comparisons and optionally square roots. Initially (1838) it was conceived as a difference engine curved backOne-way function (1,864 words) [view diff] case mismatch in snippet view article find links to article

specific member of the Rabin collection. It can be shown that extracting square roots, i.e. inverting the Rabin function, is computationally equivalent toRobert Shelton (critic) (986 words) [view diff] exact match in snippet view article

for publication by Omnibus Press in May 2021. The folk music charity Square Roots Productions was midwife to the project. In the 1969 Shelton had movedConcurrence (quantum computing) (638 words) [view diff] case mismatch in snippet view article

Alternatively, the λ i {\displaystyle \lambda _{i}} 's represent the square roots of the eigenvalues of the non-Hermitian matrix ρ ρ ~ {\displaystyle \rhoClifford parallel (581 words) [view diff] case mismatch in snippet view article find links to article

every point is on two lines, each contained in the surface. Given two square roots of minus one in the quaternions, written r and s, the Clifford surfaceR4600 (815 words) [view diff] case mismatch in snippet view article find links to article

whereas double precision division have a 61-cycle latency and throughput. Square roots have a latency and throughput is one cycle less than comparative divideWord problem (mathematics education) (1,631 words) [view diff] case mismatch in snippet view article

Babylonian times. Apart from a few procedure texts for finding things like square roots, most Old Babylonian problems are couched in a language of measurementMethods of successive approximation (52 words) [view diff] case mismatch in snippet view article find links to article

approximation include the following: Babylonian method, for finding square roots of numbers Fixed-point iteration Means of finding zeros of functions:Casio V.P.A.M. calculators (1,262 words) [view diff] case mismatch in snippet view article find links to article

display of expressions of fractions, exponents, logarithms, powers and square roots etc. as they are written in a standard textbook. Natural Display usesPartial differential equation (6,357 words) [view diff] case mismatch in snippet view article find links to article

contrast to the earlier examples, this PDE is nonlinear, owing to the square roots and the squares. A linear PDE is one such that, if it is homogeneousDifference of two squares (1,830 words) [view diff] case mismatch in snippet view article find links to article

least moving them), applying to division by some combinations involving square roots. For example: The denominator of 5 3 + 4 {\displaystyle {\dfrac {5}{{\sqrtPartial function (2,035 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \mathbb {R} } : because negative real numbers do not have real square roots, the operation can be viewed as a partial function from R {\displaystylePrime number (14,051 words) [view diff] case mismatch in snippet view article find links to article

proving quadratic reciprocity, a statement that concerns the existence of square roots modulo integer prime numbers. Early attempts to prove Fermat's Last TheoremSecurity of cryptographic hash functions (1,949 words) [view diff] exact match in snippet view article find links to article

solvable in polynomial time Discrete Logarithm Problem Finding Modular Square Roots Integer Factorization Problem Subset Sum Problem Current collision-resistantPi (17,168 words) [view diff] case mismatch in snippet view article find links to article

cannot be expressed using any finite combination of rational numbers and square roots or n-th roots (such as 3√31 or √10). Second, since no transcendentalFunctional equation (1,635 words) [view diff] case mismatch in snippet view article find links to article

) {\displaystyle f(f(x))=g(x)} , which characterizes the functional square roots of the function g f ( x + y ) = f ( x ) + f ( y ) {\displaystyle f(x+y)=f(x)+f(y)\AVX-512 (3,833 words) [view diff] case mismatch in snippet view article find links to article

fraction bits VRSQRT14PD, VRSQRT14PS Compute approximate reciprocals of square roots of packed float32/float64 values VRSQRT14SD, VRSQRT14SS Compute approximateCovariance matrix (5,403 words) [view diff] case mismatch in snippet view article find links to article

needed; the directions of the arrows correspond to the eigenvectors of this covariance matrix and their lengths to the square roots of the eigenvalues.Metaballs (687 words) [view diff] case mismatch in snippet view article find links to article

Wyvill brothers provides higher degree of smoothness and still avoids square roots.[citation needed] A simple generalization of metaballs is to apply theJoshua Abrams (musician) (1,004 words) [view diff] exact match in snippet view article

While living in Philadelphia in the late 1980s, Abrams was a member of Square Roots, a street music group that developed into The Roots. He moved to ChicagoPythagorean theorem (12,662 words) [view diff] case mismatch in snippet view article find links to article

squared Euclidean distance, or SED) is used, the resulting equation avoids square roots and is simply a sum of the SED of the coordinates: ( a 1 − b 1 ) 2 +Mertens conjecture (1,338 words) [view diff] case mismatch in snippet view article find links to article

graph shows the Mertens function M ( n ) {\displaystyle M(n)} and the square roots ± n {\displaystyle \pm {\sqrt {n}}} for n ≤ 10 , 000 {\displaystyle n\leqWalt Kelly (2,702 words) [view diff] exact match in snippet view article find links to article

two, three, and four subtitled At the Mercy of Elephants, Diggin' fo' Square Roots and Dreamin' of a Wide Catfish, respectively. In 2003 Reaction RecordsLidell Townsell (332 words) [view diff] exact match in snippet view article find links to article

Party Records (TRAX, 2004) Duh Duh Da (TRAX, 2004) I'll Make U Dance (Square Roots, 2004) Lost Acid Tracks EP (Nu Soul, 2009) Do It (Right) Shit Robot FeatAnalog computer (6,524 words) [view diff] case mismatch in snippet view article find links to article

development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithmsMurderous Maths (1,848 words) [view diff] case mismatch in snippet view article find links to article

Easy Questions, Evil Answers, ISBN 1-407-11451-4 (formulas, working out square roots by hand, π, Pythagoras, paradoxes, problem solving, metric prefixes,Lidell Townsell (332 words) [view diff] exact match in snippet view article find links to article

Party Records (TRAX, 2004) Duh Duh Da (TRAX, 2004) I'll Make U Dance (Square Roots, 2004) Lost Acid Tracks EP (Nu Soul, 2009) Do It (Right) Shit Robot FeatNoncentral chi-squared distribution (3,645 words) [view diff] case mismatch in snippet view article find links to article

Usability of these transformations may be hampered by the need to take the square roots of negative numbers. Two-sided normal regression tolerance intervalsDefinable set (1,229 words) [view diff] case mismatch in snippet view article find links to article

set of nonnegative reals, since these are the only reals that possess square roots: φ = ∃ y ( y ⋅ y ≡ x ) . {\displaystyle \varphi =\exists y(y\cdot y\equivAngle trisection (3,158 words) [view diff] case mismatch in snippet view article find links to article

whereas ruler-and-compass can construct only quadratic extensions (square roots). There are a number of simple linkages which can be used to make anMinimal polynomial (field theory) (1,214 words) [view diff] case mismatch in snippet view article

cyclotomic polynomials. The minimal polynomial in Q[x] of the sum of the square roots of the first n prime numbers is constructed analogously, and is calledCubic equation (10,131 words) [view diff] case mismatch in snippet view article find links to article

and any cube root, respectively (every nonzero complex number has two square roots and three cubic roots). The sign "±" before the square root is eitherEquating coefficients (1,101 words) [view diff] case mismatch in snippet view article find links to article

{c}}=d+e+2{\sqrt {de}}.} To find d and e we equate the terms not involving square roots, so a = d + e , {\displaystyle a=d+e,} and equate the parts involvingDe Moivre's formula (2,400 words) [view diff] case mismatch in snippet view article find links to article

consistent in this case. On the other hand, the values 1 and −1 are both square roots of 1. More generally, if z and w are complex numbers, then ( cos zGeorge Pólya Award (121 words) [view diff] exact match in snippet view article find links to article

2000 Martin Gardner The Asymmetric Propeller 2000 Ezra (Bud) Brown Square Roots From 1; 24, 51, 10 to Dan Shanks 1999 David Bleecker and Larry WallenK-d tree (3,901 words) [view diff] case mismatch in snippet view article find links to article

the algorithm uses squared distances for comparison to avoid computing square roots. Additionally, it can save computation by holding the squared currentPolynomial transformation (1,076 words) [view diff] case mismatch in snippet view article find links to article

is termed depressed. This already suffices to solve the quadratic by square roots. In the case of the cubic, Tschirnhaus transformations replace the variableCUDA (3,856 words) [view diff] case mismatch in snippet view article find links to article

by setting compiler flags to disable accurate divisions and accurate square roots, and enable flushing denormal numbers to zero. Unlike OpenCL, CUDA-enabledLyapunov exponent (3,166 words) [view diff] case mismatch in snippet view article find links to article

(}X(t){\big )}\}_{1}^{n}} of the matrix X ( t ) {\displaystyle X(t)} are the square roots of the eigenvalues of the matrix X ( t ) ∗ X ( t ) {\displaystyle X(t)^{*}X(t)}Number theory (10,718 words) [view diff] case mismatch in snippet view article find links to article

can be expressed in terms of the four basic operations together with square roots, cubic roots, etc.) if and only if the extension of the rationals byBLAKE (hash function) (2,773 words) [view diff] case mismatch in snippet view article

by taking the first 64 bits of the fractional parts of the positive square roots of the first eight prime numbers. IV0 = 0x6a09e667f3bcc908 // Frac(sqrt(2))Chuck Hedges (295 words) [view diff] exact match in snippet view article find links to article

(1976) Chuck Hedges, Johnny Varro, Ray Leatherwood, Gene Estes: The Square Roots of Jazz (1984) No Greater Love (Arbors, 1992), with Eddie Higgins, BobAbelian variety (2,908 words) [view diff] case mismatch in snippet view article find links to article

of research. The standard forms for elliptic integrals involved the square roots of cubic and quartic polynomials. When those were replaced by polynomialsMatrix (mathematics) (12,317 words) [view diff] case mismatch in snippet view article

arising in solving linear differential equations, matrix logarithms and square roots of matrices. To avoid numerically ill-conditioned situations, furtherHadamard product (matrices) (2,559 words) [view diff] case mismatch in snippet view article

1007/s003620100074. S2CID 121385730. Reams, Robert (1999). "Hadamard inverses, square roots and products of almost semidefinite matrices". Linear Algebra and ItsENIAC (7,802 words) [view diff] case mismatch in snippet view article find links to article

numbers had fewer than 10 digits, the operation was faster. Division and square roots took 13(d+1) cycles, where d is the number of digits in the result (quotientKatie Walder (180 words) [view diff] exact match in snippet view article find links to article

Be You Tanya TV film 2016 Skirtchasers Chelsea Samuels TV film 2016 Square Roots Ruth TV film 2017 Lethal Weapon Denise Barnes Episode: "El Gringo Loco"Field (mathematics) (10,374 words) [view diff] case mismatch in snippet view article

field Q of rational numbers. The illustration shows the construction of square roots of constructible numbers, not necessarily contained within Q. Using theVersor (2,236 words) [view diff] case mismatch in snippet view article find links to article

vectors of length one (unit vectors). The right versors form a sphere of square roots of −1 in the quaternion algebra. The generators i, j, and k are examples700 (number) (4,110 words) [view diff] case mismatch in snippet view article

{\displaystyle \cos \left({\frac {2\pi }{771}}\right)} can be written in terms of square roots. 772 = 22 × 193, 772!!!!!!+1 is prime 773 = prime number, EisensteinBhāskara II (3,640 words) [view diff] case mismatch in snippet view article find links to article

chapters. It was the first text to recognize that a positive number has two square roots (a positive and negative square root). His work Bījaganita is effectivelyInvertible matrix (6,566 words) [view diff] case mismatch in snippet view article find links to article

the pair of sequences of inverse matrices used in obtaining matrix square roots by Denman–Beavers iteration; this may need more than one pass of theSt. Thomas' Episcopal School (2,117 words) [view diff] case mismatch in snippet view article find links to article

of pre-algebra and elementary algebra concepts: fractions, integers, square roots and exponents, decimals, and the Cartesian coordinate system, among othersPythagorean addition (1,653 words) [view diff] case mismatch in snippet view article find links to article

+-+ respectively. Moler, Cleve; Morrison, Donald (1983). "Replacing square roots by Pythagorean sums". IBM Journal of Research and Development. 27 (6):Vera Faddeeva (882 words) [view diff] case mismatch in snippet view article find links to article

linear equations and the inversion of matrices, and explained computing square roots and eigenvalues and eigenvectors of a matrix. Faddeeva had continuedSoftware patents under United Kingdom patent law (3,295 words) [view diff] no match in snippet view article find links to article

new computer chip used to implement a faster method for calculating square-roots was rejected as not being an invention in the UK (Gale's Application)Mental calculator (1,605 words) [view diff] case mismatch in snippet view article find links to article

reporter/producer Lisa Miller can mentally calculate products, quotients, and square roots effortlessly and almost instantly, on demand. In the 1997 Sci-Fi thrillerPrincipal component analysis (13,546 words) [view diff] case mismatch in snippet view article find links to article

the Eckart–Young theorem [1936]. The singular values (in Σ) are the square roots of the eigenvalues of the matrix XTX. Each eigenvalue is proportionalDefinite matrix (8,384 words) [view diff] case mismatch in snippet view article find links to article

D^{\frac {1}{2}}} as the diagonal matrix whose entries are non-negative square roots of eigenvalues. Then M = Q − 1 D Q = Q ∗ D Q = Q ∗ D 1 2 D 1 2 Q = QAlberto Coto García (328 words) [view diff] exact match in snippet view article find links to article

Memoriad Mental Additions World Champion: İstanbul 2008 Memoriad Mental Square Roots World Champion: İstanbul 2008 World champion in addition: Magdeburg 2010Impedance parameters (1,634 words) [view diff] case mismatch in snippet view article find links to article

{\sqrt {y}}=({\sqrt {z}})^{-1}} is the corresponding diagonal matrix of square roots of characteristic admittances. In these expressions the matrices representedHan dynasty (17,956 words) [view diff] case mismatch in snippet view article find links to article

mathematical achievements include solving problems with right-angle triangles, square roots, cube roots, and matrix methods, finding more accurate approximationsThe Number Devil (1,584 words) [view diff] case mismatch in snippet view article find links to article

Devil teaches Robert about rutabagas, another fictional term to depict square roots, at a beach. For a time after the fourth night, Robert cannot find thePOVM (3,247 words) [view diff] case mismatch in snippet view article find links to article

obtain a projective measurement that physically realises this POVM. The square roots of the POVM elements are given by F ψ = 1 1 + | ⟨ φ | ψ ⟩ | | φ ⊥ ⟩ ⟨Friedmann–Lemaître–Robertson–Walker metric (4,231 words) [view diff] case mismatch in snippet view article find links to article

k {\displaystyle {\sqrt {k}}} is one of the imaginary, zero or real square roots of k. These definitions are valid for all k. When k = 0 one may writeSkew-Hamiltonian matrix (278 words) [view diff] exact match in snippet view article find links to article

Fassbender, D. Steven Mackey, Niloufer Mackey and Hongguo Xu Hamiltonian Square Roots of Skew-Hamiltonian Matrices, Linear Algebra and its Applications 287Elementary algebra (5,509 words) [view diff] case mismatch in snippet view article find links to article

radical equation is one that includes a radical sign, which includes square roots, x , {\displaystyle {\sqrt {x}},} cube roots, x 3 {\displaystyle {\sqrt[{3}]{x}}}Kenosha, Wisconsin (8,641 words) [view diff] exact match in snippet view article find links to article

have warehouses and distribution centers located in Kenosha. In 2022, Square Roots farm opened a fully indoor hydroponic facility within refurbished shippingSum of two squares theorem (548 words) [view diff] case mismatch in snippet view article find links to article

32, ... They form the set of all norms of Gaussian integers; their square roots form the set of all lengths of line segments between pairs of pointsCauchy–Schwarz inequality (6,635 words) [view diff] case mismatch in snippet view article find links to article

CS}}\\&\leq (\|\mathbf {u} \|+\|\mathbf {v} \|)^{2}.&&\end{alignedat}}} Taking square roots gives the triangle inequality: ‖ u + v ‖ ≤ ‖ u ‖ + ‖ v ‖ . {\displaystyleLists of integrals (5,584 words) [view diff] exact match in snippet view article find links to article

Online Math Notes A. Dieckmann, Table of Integrals (Elliptic Functions, Square Roots, Inverse Tangents and More Exotic Functions): Indefinite Integrals DefiniteJames Thomson Bottomley (530 words) [view diff] case mismatch in snippet view article find links to article

comprising logarithmic and trigonometrical tables, and tables of squares, square roots, and reciprocals. "The University of Glasgow Story; James Thomson Bottomley"Suken (244 words) [view diff] case mismatch in snippet view article find links to article

numbers Inequalities Simultaneous equations Congruency and similarities Square roots Factorization Quadratic equations and functions The Pythagorean theoremIon beam mixing (961 words) [view diff] case mismatch in snippet view article find links to article

the ion beam on a target. The amount of mixing is proportional to the square roots of time, mass and ion dose. At temperatures below 100 °C for most implantedBenford's law (7,128 words) [view diff] case mismatch in snippet view article find links to article

(i.e. increasing accuracy as the process continues through time). The square roots and reciprocals of successive natural numbers do not obey this law. PrimeUltraSPARC III (1,238 words) [view diff] case mismatch in snippet view article find links to article

instructions such as adds while the other executes multiplies, divides and square roots. The UltraSPARC III has split primary instruction and data caches. ThePatrick Doyon (311 words) [view diff] exact match in snippet view article find links to article

professional film. Doyon had previously created a three-minute animated short Square Roots in 2006, while enrolled in the NFB's Hothouse program for young animatorsAdmittance parameters (1,679 words) [view diff] case mismatch in snippet view article find links to article

{\sqrt {z}}=({\sqrt {y}})^{-1}} is the corresponding diagonal matrix of square roots of characteristic impedances. In these expressions the matrices representedHensel's lemma (9,041 words) [view diff] case mismatch in snippet view article find links to article

using the more general version of Hensel's lemma (an example with 2-adic square roots of 17 is given later). To make the discussion above more explicit, letDNA computing (4,866 words) [view diff] case mismatch in snippet view article find links to article

nucleic-acid-based integrated circuits. One of these chips can compute whole square roots. A compiler has been written in Perl. The slow processing speed of aLangmuir (unit) (872 words) [view diff] case mismatch in snippet view article

molecular mass of adsorbing gas. However, the dependence is only on the square roots of m and T. Gas adsorption experiments typically operate around ambientMrigya (427 words) [view diff] case mismatch in snippet view article find links to article

Busan International Rock Festival - 2011 Vancouver Folk Festival - 2012 Square roots festival, Chicago - 2012 Bibliotheca Alexandrina, Alexandria - 2013 HeraldAlexander P. Yefremov (299 words) [view diff] case mismatch in snippet view article find links to article

2007, ISBN 978-1-59973-042-4, p. 208–219 A. Yefremov: Bi-quaternion square roots, rotational relativity, and dual space-time intervals, Gravitation &Polar decomposition (4,145 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \lbrace xi+yj+zk\in H:x^{2}+y^{2}+z^{2}=1\rbrace } of square roots of minus one. Given any r on this sphere, and an angle −π < a ≤ π, theJulia set (5,459 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle z_{n-1}={\sqrt {z_{n}-c}}.} At each step, one of the two square roots is selected at random. Note that certain parts of the Julia set are quitePer Enflo (4,342 words) [view diff] case mismatch in snippet view article find links to article

doi:10.1007/bf02589550. Enflo, Per (1970a). "Uniform structures and square roots in topological groups I". Israel Journal of Mathematics. 8 (3): 230–252Rhythm of Structure (3,684 words) [view diff] exact match in snippet view article find links to article

Systems in Isotropic Space-Map Projection: The Cube by Agnes Denes, Square Roots of a Tree by John Sims, Squaring the Circle: Heaven in Earth by Pam TuczynTimeline of Indian history (1,233 words) [view diff] case mismatch in snippet view article find links to article

manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and quadratic equations, and rules for summingJan Gullberg (949 words) [view diff] case mismatch in snippet view article find links to article

mediation". He admires the "efficient" Babylonian method of finding square roots, using division and averaging. He learns from Gullberg how to multiplyDonkey Kong (video game) (10,304 words) [view diff] exact match in snippet view article

throughout the 1980s and beyond. Bienaimé, Pierre (January 13, 2012). "Square Roots: Donkey Kong (NES)". Nintendojo. Archived from the original on FebruarySchoof's algorithm (4,098 words) [view diff] exact match in snippet view article find links to article

R. Schoof: Elliptic Curves over Finite Fields and the Computation of Square Roots mod p. Math. Comp., 44(170):483–494, 1985. Available at http://www.matUncertainty principle (17,870 words) [view diff] case mismatch in snippet view article find links to article

state rather than for the quantum state, and compute an average of their square roots. The following expression is stronger than the Robertson–SchrödingerTravelling salesman problem (11,565 words) [view diff] case mismatch in snippet view article find links to article

have integer coordinates, their distances generally take the form of square roots, and the length of a tour is a sum of radicals, making it difficult toR8000 (1,841 words) [view diff] no match in snippet view article find links to article

latencies of 14 and 20 cycles, respectively; and single and double precision square-roots have latencies of 14 and 23 cycles, respectively. The streaming cacheBaillie–PSW primality test (2,399 words) [view diff] case mismatch in snippet view article find links to article

because perfect squares are easy to detect using Newton's method for square roots. If step 3 fails to produce a D quickly, one should check whether n is1616 (6,293 words) [view diff] case mismatch in snippet view article find links to article

efficient method of finding logarithms, by the continued extraction of square roots. Moralist writer John Deacon publishes a quarto entitled Tobacco TorturedSpacetime (27,792 words) [view diff] case mismatch in snippet view article find links to article

intervals in Minkowski spacetime can be negative. Rather than deal with square roots of negative numbers, physicists customarily regard s 2 {\displaystyleIndex ellipsoid (2,605 words) [view diff] case mismatch in snippet view article find links to article

_{z}}}~,} indicating that the semiaxes of the index ellipsoid are the square roots of the principal dielectric constants. Substituting these expressionsRice's theorem (3,014 words) [view diff] case mismatch in snippet view article find links to article

t. We could have had a method for recognizing programs for computing square roots, or programs for computing the monthly payroll, or programs that haltR10000 (2,608 words) [view diff] case mismatch in snippet view article find links to article

cycles for single precision and double precision respectively. Reciprocal square roots have longer latencies, 30 to 52 cycles for single precision (32-bit)Abu Kamil (1,966 words) [view diff] case mismatch in snippet view article find links to article

of application to geometry, often involving an unknown variable and square roots. The second chapter deals with the six types of problems found in Al-Khwarizmi'sBlackmer RMS detector (945 words) [view diff] case mismatch in snippet view article find links to article

produce linear, not logarithmic, output. Analog computation of squares and square roots was performed using either expensive variable-transconductance analogOrthogonal group (7,901 words) [view diff] case mismatch in snippet view article find links to article

_{V}\rightarrow \mathrm {O_{V}} \rightarrow 1} Here μ2 is the algebraic group of square roots of 1; over a field of characteristic not 2 it is roughly the same asAleksandr Kotelnikov (624 words) [view diff] case mismatch in snippet view article find links to article

\mathbb {R} ^{3}} , three-dimensional Euclidean space: If r is one of the square roots of minus one in H {\displaystyle \mathbb {H} } , then an underline (L. M. Milne-Thomson (686 words) [view diff] exact match in snippet view article find links to article

constructed with L. J. Comrie and published in 1931, Standard Table of Square Roots (1932), and Jacobian Elliptic Function Tables (1932). Later, Milne-ThomsonDynamic rectangle (1,597 words) [view diff] case mismatch in snippet view article find links to article

irrational and geometric fractions as ratios, such as the golden ratio or square roots. Hambidge distinguishes these from rectangles with rational proportionsPenilaian Menengah Rendah (2,780 words) [view diff] case mismatch in snippet view article find links to article

Percentages Financial mathematics Lines and angles Bearing Squares, square roots, cubes and cube roots Indices Surds Polygons Statistics Pythagoras' theoremAnomalous cancellation (862 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle n} is a square. Let n = k 2 {\displaystyle n=k^{2}} . Taking square roots and rearranging yields a k = ( k + 1 ) b {\displaystyle ak=(k+1)b} .List of Indian inventions and discoveries (19,832 words) [view diff] case mismatch in snippet view article find links to article

occurring in one complex problem. Brahmagupta also used abbreviations for square roots and cube roots. Seshadri constant: In algebraic geometry, a SeshadriLaplacian matrix (4,923 words) [view diff] case mismatch in snippet view article find links to article

the diagonal matrix whose diagonal entries are the reciprocals of the square roots of the diagonal entries of D. If all the edge weights are nonnegativeR5000 (1,810 words) [view diff] case mismatch in snippet view article find links to article

Single-precision divides have a 21-cycle latency and a 19-cycle throughput, while square roots have a 26-cycle latency and a 38-cycle throughput. Division and square-rootX86 assembly language (5,704 words) [view diff] case mismatch in snippet view article find links to article

addition, subtraction, negation, multiplication, division, remainder, square roots, integer truncation, fraction truncation, and scale by power of two.Chinese mathematics (8,258 words) [view diff] case mismatch in snippet view article find links to article

position method for finding roots and the extraction of approximate square roots Conversion between different units The first reference to a book beingVector logic (3,483 words) [view diff] case mismatch in snippet view article find links to article

extended for arbitrary orthonormal truth values. There are, in fact, two square roots of NOT: A = ( N ) 1 = 1 2 ( 1 + i ) I + 1 2 ( 1 − i ) N {\displaystyleK-minimum spanning tree (1,056 words) [view diff] case mismatch in snippet view article find links to article

known to belong to NP, because of the difficulty of comparing sums of square roots; instead it lies in the class of problems reducible to the existentialClifford algebra (9,182 words) [view diff] case mismatch in snippet view article find links to article

connecting homomorphism on cohomology. Writing μ2 for the algebraic group of square roots of 1 (over a field of characteristic not 2 it is roughly the same asAlan Schwarz (2,672 words) [view diff] case mismatch in snippet view article find links to article

Statistical Reporting award. Schwarz's father taught him how to compute square roots when he was 4 years old. At the University of Pennsylvania, where heMath Girls (2,067 words) [view diff] case mismatch in snippet view article find links to article

inequalities The relationship between arithmetic and geometric means Square roots Derivatives Derivative functions Limits Finite difference method FallingBarlow's law (663 words) [view diff] case mismatch in snippet view article find links to article

of the lengths and directly as the diameters of the wires or as the square roots of their sections.' Schiffer, Michael (2008). Power Struggles: ScientificFrederick V. Waugh (424 words) [view diff] case mismatch in snippet view article find links to article

Association of America for a paper on the rational approximation of square roots. A collection of Waugh's selected works was published by the UniversityAmpere balance (547 words) [view diff] case mismatch in snippet view article find links to article

pair of weights and by a square root table, so that the product of the square roots of the number corresponding to the position of the sliding weight andRené Schoof (412 words) [view diff] case mismatch in snippet view article find links to article

Vergata René Schoof: Elliptic curves over finite fields and the calculation of square roots mod p, Mathematics of Computation, No. 44, 1985, 483–494.Hyperbola (12,781 words) [view diff] case mismatch in snippet view article find links to article

{\sqrt {(x-c)^{2}+y^{2}}}-{\sqrt {(x+c)^{2}+y^{2}}}=\pm 2a\ .} Remove the square roots by suitable squarings and use the relation b 2 = c 2 − a 2 {\displaystyleBessel's correction (4,038 words) [view diff] case mismatch in snippet view article find links to article

with Bessel's correction) The standard deviations will then be the square roots of the respective variances. Since the square root introduces bias, theVersine (4,509 words) [view diff] case mismatch in snippet view article find links to article

having a table of the haversine removed the need to compute squares and square roots. An early utilization by José de Mendoza y Ríos of what later would beKalman filter (19,869 words) [view diff] case mismatch in snippet view article find links to article

on the relative efficiency is somewhat misleading, as it assumed that square roots were much more time-consuming than divisions,: 69 while on 21st-centuryWeyl equation (4,597 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \eta =\zeta ~.} These two Majorana operators are thus "square roots" of the Klein–Gordon operator. The equations are obtained from the LagrangianFeige–Fiat–Shamir identification scheme (779 words) [view diff] case mismatch in snippet view article find links to article

until Victor is satisfied that Peggy does indeed possess the modular square roots ( s i {\displaystyle s_{i}} ) of his v i {\displaystyle v_{i}} numbersLucas sequence (3,881 words) [view diff] case mismatch in snippet view article find links to article

of the form 2n + 1, which include the Fermat numbers Un(6, 1) : The square roots of the square triangular numbers. Un(x,−1) : Fibonacci polynomials Vn(xSolution of triangles (3,625 words) [view diff] case mismatch in snippet view article find links to article

list the results for the question of solvability using no higher than square roots (i.e., constructibility) for each of the 95 distinct cases; 63 of theseList of Polish people (1,618 words) [view diff] case mismatch in snippet view article find links to article

Abraham Stern, first computing-machine and device for calculating the square roots of numbers Wacław Struszyński, seaborne direction finding antenna, whichGolden age of arcade video games (10,864 words) [view diff] exact match in snippet view article find links to article

States: 67,000 of Donkey Kong Bienaimé, Pierre (January 13, 2012). "Square Roots: Donkey Kong (NES)". Nintendojo. Retrieved April 8, 2012. Donkey KongVan Cittert–Zernike theorem (4,658 words) [view diff] case mismatch in snippet view article find links to article

Normalization of the mutual coherence function to the product of the square roots of the intensities of the two electric fields yields the complex degreeTimeline of mathematical innovation in South and West Asia (1,763 words) [view diff] case mismatch in snippet view article find links to article

360-375, pp. 360–375, ISBN 978-1-4051-3251-0. Henderson, David W. (2000), "Square roots in the Sulba Sutras", in Gorini, Catherine A. (ed.), Geometry at Work:Low-discrepancy sequence (3,909 words) [view diff] case mismatch in snippet view article find links to article

for each dimension. A convenient set of values that are used, is the square roots of primes from two up, all taken modulo 1: c = 2 , 3 , 5 , 7 , 11 , …History of computing hardware (16,270 words) [view diff] case mismatch in snippet view article find links to article

perform all four arithmetic operations, plus comparisons and optionally square roots. Initially it was conceived as a difference engine curved back upon itselfAbraham Stern (inventor) (598 words) [view diff] case mismatch in snippet view article

mechanical calculator, perfected in 1817, which could calculate the square roots of numbers. This attracted wide attention, and led to his being electedArithmetic function (7,503 words) [view diff] case mismatch in snippet view article find links to article

that differ only in the order of the summands or in the signs of the square roots are counted as different. r k ( n ) = | { ( a 1 , a 2 , … , a k ) : nRoman surface (2,791 words) [view diff] case mismatch in snippet view article find links to article

of U, V, W are positive, or else exactly two are negative. So these square roots are of positive numbers.) It is easy to use (*) to confirm that (**)Trachtenberg system (6,482 words) [view diff] case mismatch in snippet view article find links to article

answer Chapter 5 Division – Speed and accuracy Chapter 6 Squares and square roots Chapter 7 Algebraic description of the method Quotes: "A revolutionaryQuartic equation (5,530 words) [view diff] case mismatch in snippet view article find links to article

both signs of square root, as long as the same sign is taken for both square roots. A ± is redundant, as it would be absorbed by another ± a few equationsOne Two Three... Infinity (1,537 words) [view diff] case mismatch in snippet view article find links to article

sum to two primes." It was an epithet of Gerolamo Cardano that stuck: square roots of negative numbers are imaginary. The Argand diagram is displayed, andTechnologies in 2001: A Space Odyssey (3,132 words) [view diff] case mismatch in snippet view article find links to article

reproducible results using invariant established methods (such as computing square roots). A heuristic approach that usually works within a tolerable margin ofLiouville number (4,893 words) [view diff] case mismatch in snippet view article find links to article

measure of any irrational algebraic number is exactly 2. Examples include square roots like 2 , 3 {\displaystyle {\sqrt {2}},{\sqrt {3}}} and 5 {\displaystyleOrthogonal coordinates (3,267 words) [view diff] case mismatch in snippet view article find links to article

}{=}}\ {\sqrt {g_{kk}(\mathbf {q} )}}=|\mathbf {e} _{k}|} equal the square roots of the diagonal components of the metric tensor, or the lengths of theMechanical calculator (8,793 words) [view diff] case mismatch in snippet view article find links to article

additions and subtractions. Friden made a calculator that also provided square roots, basically by doing division, but with added mechanism that automaticallyApproximations of π (10,726 words) [view diff] case mismatch in snippet view article find links to article

in applying the method lies in obtaining good approximations for the square roots that are involved. Trigonometry, in the form of a table of chord lengthsList of historic Indian texts (233 words) [view diff] case mismatch in snippet view article find links to article

determining the rules for addition, subtraction, division, multiplication, square roots, cube roots, and quadratic equations Śrīpati 1056 CE Mitākṣarā LegalTangent half-angle formula (2,919 words) [view diff] case mismatch in snippet view article find links to article

=1-2\sin ^{2}\alpha =2\cos ^{2}\alpha -1} , rearranging, and taking the square roots yields | sin α | = 1 − cos 2 α 2 {\displaystyle |\sin \alpha |={\sqrtNational Assessment of Educational Progress (3,689 words) [view diff] case mismatch in snippet view article find links to article

criticism. Math answers have penalized students who understand negative square roots, interest on loans, and errors in extrapolating a graph beyond the dataUdwadia–Kalaba formulation (3,155 words) [view diff] case mismatch in snippet view article find links to article

^{-1/2}} is the diagonal matrix whose diagonal elements are the inverse square roots of the eigenvalues corresponding to the eigenvectors in W {\displaystyle600-cell (21,444 words) [view diff] case mismatch in snippet view article find links to article

circles, the decagons and pentagons. The new chord lengths are necessarily square roots of fractions, but very special fractions related to the golden ratioΠ pad (1,197 words) [view diff] case mismatch in snippet view article find links to article

Π pad is used. In this case, the impedance matching terms inside the square roots all cancel and, L Π = L L 1 L L 2 = e 2 γ L = e γ Π {\displaystyle L_{\mathrmInverse iteration (2,070 words) [view diff] case mismatch in snippet view article find links to article

not be practical. Also transformation to the Hessenberg form involves square roots and the division operation, which are not universally supported by hardwareRiemann mapping theorem (5,942 words) [view diff] case mismatch in snippet view article find links to article

⇒ (6) because if γ is a piecewise closed curve and fn are successive square roots of z − w for w outside G, then the winding number of fn ∘ γ about w isGenius Junior (1,180 words) [view diff] case mismatch in snippet view article find links to article

or divide. In the finals, the problems will include squares, cubes, square roots, and/or cube roots. The contestants must spell words backwards. In theBKM algorithm (1,999 words) [view diff] case mismatch in snippet view article find links to article

1972). "Automatic computation of exponentials, logarithms, ratios and square roots". IBM Journal of Research and Development. San Jose, California, USA;Norman H. Anning (643 words) [view diff] exact match in snippet view article find links to article

1949-8594.1916.tb01570.x. Norman H. Anning (1915). "To Find Approximate Square Roots". School Science and Mathematics. 15 (3): 245–246. doi:10.1111/j.1949-8594Plimpton 322 (5,866 words) [view diff] case mismatch in snippet view article find links to article

computing the factor-reduced core was part of the process of calculating square roots in Old Babylonian mathematics. According to Friberg, "it was never thePlimpton 322 (5,866 words) [view diff] case mismatch in snippet view article find links to article

computing the factor-reduced core was part of the process of calculating square roots in Old Babylonian mathematics. According to Friberg, "it was never theFreight Farms (881 words) [view diff] exact match in snippet view article find links to article

Major sales included Google, Ford Foundation, Sodexo, Compass Group, and Square Roots. In February 2019, Freight Farms announced that after five years andInequality of arithmetic and geometric means (7,141 words) [view diff] case mismatch in snippet view article find links to article

Visual proof that (x + y)2 ≥ 4xy. Taking square roots and dividing by two gives the AM–GM inequality.List of important publications in mathematics (10,137 words) [view diff] case mismatch in snippet view article find links to article

positive numbers, rules for dealing the number zero, a method for computing square roots, and general methods of solving linear and some quadratic equations,Crossed ladders problem (2,191 words) [view diff] case mismatch in snippet view article find links to article

according to the top diagram. As the solutions to the equation involve square roots, negative roots are equally valid. They can be interpreted as both laddersTheodor Vahlen (1,826 words) [view diff] case mismatch in snippet view article find links to article

construction of his 2n dimensional algebra with n − 1 anti-commuting square roots of −1. Vahlen also recounts split-biquaternions and parabolic biquaternionsProofs of trigonometric identities (5,697 words) [view diff] case mismatch in snippet view article find links to article

chosen properly—note that if 2π is added to θ, the quantities inside the square roots are unchanged, but the left-hand-sides of the equations change sign.Margaret Maxfield (852 words) [view diff] case mismatch in snippet view article find links to article

America for a paper with her father on the rational approximation of square roots. "Margaret W. Maxfield", Placerville Mountain Democrat, December 23,Graeme Gunn (1,918 words) [view diff] exact match in snippet view article find links to article

Bernstone, Rachel "Pulse" In Design; Issue 47 (2011) pp. 196–197 Rizzo R, "Square Roots" Architectural Review Australia; Summer 2010/2011 pp. 78–85 HarrisonCourt of the Lions (6,747 words) [view diff] case mismatch in snippet view article find links to article

postulates, the rectangles used in the construction may have been based on square roots and surds. The pavilions are also supported by slender columns formingSchur product theorem (1,664 words) [view diff] no match in snippet view article find links to article

{\displaystyle N} are positive definite, and so Hermitian. We can consider their square-roots M 1 2 {\displaystyle M^{\frac {1}{2}}} and N 1 2 {\displaystyle N^{\fracExistential theory of the reals (3,727 words) [view diff] case mismatch in snippet view article find links to article

existential quantifiers, and one that uses extra symbols for division, square roots, and the number 2 that are not allowed in the first-order theory of the1610s (21,956 words) [view diff] case mismatch in snippet view article find links to article

efficient method of finding logarithms, by the continued extraction of square roots. Moralist writer John Deacon publishes a quarto entitled Tobacco TorturedGeneralized continued fraction (8,748 words) [view diff] case mismatch in snippet view article find links to article

trovar la radice quadra delli numeri [A treatise on a quick way to find square roots of numbers]. Chrystal, George (1999). Algebra, an Elementary Text-bookThe High Road to China (The Drew Carey Show) (1,973 words) [view diff] exact match in snippet view article

an A&W near to his hotel. Brownfield, Paul (September 20, 1998). "The Square Roots of This Duo's Success". Los Angeles Times. Retrieved February 24, 2014Marc Laurick (807 words) [view diff] exact match in snippet view article find links to article

Morris, Khan Jamal, Rob Brown, Marc Ribot, Rufus Harley, Tani Tabbal, and Square Roots (later The Roots). In 1997, he assisted Scott Black with the Frank LloydBring radical (8,148 words) [view diff] case mismatch in snippet view article find links to article

numerical means, the roots of the quintic can be written in terms of square roots, cube roots, and the Bring radical, which is therefore an algebraic solutionAttosecond physics (5,994 words) [view diff] case mismatch in snippet view article find links to article

e {\displaystyle c_{e}} and c g {\displaystyle c_{g}} chosen as the square roots of the quantum probability of observing the particle in the correspondingX86 instruction listings (4,584 words) [view diff] exact match in snippet view article find links to article

Floating-Point Values and Set EFLAGS SQRTPS xmm1, xmm2/m128 0F 51 /r Compute Square Roots of Packed Single-Precision Floating-Point Values SQRTSS xmm1, xmm2/m32Ufouria: The Saga (3,228 words) [view diff] exact match in snippet view article find links to article

2021-10-25. Retrieved 2021-10-24. Brown, Luke (September 20, 2021). "Square Roots: Ufouria: The Saga — A forgotten NES diamond in the rough". NintendojoList of Egyptian inventions and discoveries (17,737 words) [view diff] case mismatch in snippet view article find links to article

possibly the Kahun Papyrus – that shows how the Egyptians extracted square roots by an inverse proportion method. 0 – By 1770 BC, the Egyptians had aSpecial cases of Apollonius' problem (2,636 words) [view diff] case mismatch in snippet view article find links to article

be constructed if and only if (iff) (something about no higher than square roots are taken). Therefore, it is important to determine whether an objectProbability bounds analysis (4,527 words) [view diff] case mismatch in snippet view article find links to article

multiplications, divisions, minima, maxima, powers, exponentials, logarithms, square roots, absolute values, etc., are commonly used in risk analyses and uncertaintyMargaret Willerding (1,267 words) [view diff] exact match in snippet view article find links to article

Integers and Their Operations; Equations and Inequalities; Squares, Square Roots, and Similar Triangles (Prindle, Weber & Schmidt, 1975) Mathematics:Derivations of the Lorentz transformations (11,544 words) [view diff] case mismatch in snippet view article find links to article

A=D=\cosh \phi \,,\quad C=B=-\sinh \phi } where the signs after the square roots are chosen so that x and t increase. The hyperbolic transformations haveMajorana equation (8,807 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \eta =\zeta ~.} These two Majorana operators are thus "square roots" of the Klein–Gordon operator. The real four-component version of theMirifici Logarithmorum Canonis Descriptio (3,355 words) [view diff] case mismatch in snippet view article find links to article

subtraction for divisional, by division by two for the extraction of square roots, and by three for cube roots ... all the heavier work of calculation2013 in science (32,904 words) [view diff] case mismatch in snippet view article find links to article

doing quantum physics'". BBC. 21 June 2013. Retrieved 22 June 2013. "Square roots? Scientists say plants are good at maths". Reuters. 23 June 2013. RetrievedSlide rule scale (1,690 words) [view diff] case mismatch in snippet view article find links to article

multiplication and division, most likely an A and B for squares and square roots, and possibly CI and K for reciprocals and cubes. In the early days ofGenetic correlation (5,887 words) [view diff] case mismatch in snippet view article find links to article

correlation is the bivariate heritability' and can be calculated as the square roots of the heritabilities multiplied by the genetic correlation. (Using aLemniscate elliptic functions (16,391 words) [view diff] case mismatch in snippet view article find links to article

lemniscate into n parts of equal length, using only basic arithmetic and square roots, if and only if n is of the form n = 2 k p 1 p 2 ⋯ p m {\displaystyleList of Rolie Polie Olie episodes (36 words) [view diff] exact match in snippet view article find links to article

gets clean in time for a date with Fifi; Zowie tries to whistle. 32 6 "Square Roots" "1 Olie, 2 Olie, 3 Olie, 4" "Switcheroo" Mike Fallows (supervising)Time-evolving block decimation (7,232 words) [view diff] case mismatch in snippet view article find links to article

_{\gamma \gamma '}^{jj'}|{j\gamma }\rangle \langle {j'\gamma '}|.} The square roots of its eigenvalues are the new λ {\displaystyle \lambda } 's. ExpressingThe Brain (game show) (6,853 words) [view diff] case mismatch in snippet view article

Challenge Formation Hu Xiaoling 88 pts. Complete the Crossword using the 40 given words. Zhou Wei 150 pts. Calculate the involution and square roots.Timeline of Indian innovation (3,496 words) [view diff] case mismatch in snippet view article find links to article

occurring in one complex problem. Brahmagupta also used abbreviations for square roots and cube roots. Chaturanga: The precursor of chess originated in IndiaOscillator representation (21,529 words) [view diff] case mismatch in snippet view article find links to article

z) is non-vanishing on H and therefore has two possible holomorphic square roots. The metaplectic group is defined as the group Mp ( 2 , R ) = { ( gRamon Picarte Mujica (2,069 words) [view diff] case mismatch in snippet view article find links to article

Imprenta Cervantes, 1891. Barlow, Peter, "Tables of squares, cubes, square roots, cube roots and reciprocals of all integers up to 12,500," fourth editionMing Antu's infinite series expansion of trigonometric functions (3,164 words) [view diff] case mismatch in snippet view article find links to article

much faster than classic Liu Hui's π algorithm which involves taking square roots. However, Jartoux did not bring along the method for deriving these infinite