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Longer titles found: Quadratic irrational number (view)

searching for Irrational number 61 found (201 total)

Diophantine approximation (4,072 words) [view diff] exact match in snippet view article find links to article

Dirichlet's approximation theorem, which implies that, for every irrational number α, there are infinitely many fractions p q {\displaystyle {\tfrac

Solving quadratic equations with continued fractions (1,766 words) [view diff] exact match in snippet view article find links to article

solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated as a decimal

Dirichlet's approximation theorem (1,155 words) [view diff] exact match in snippet view article find links to article

satisfied by infinitely many integers p and q. This shows that any irrational number has irrationality measure at least 2. The Thue–Siegel–Roth theorem

Lochs's theorem (982 words) [view diff] no match in snippet view article find links to article

exhibiting this behavior is the golden ratio—sometimes known as the "most irrational" number—whose continued fraction terms are all ones, the smallest possible

Just intonation (5,567 words) [view diff] no match in snippet view article find links to article

temperament, in which all intervals other than octaves consist of irrational-number frequency ratios. Acoustic pianos are usually tuned with the octaves

Quasi-continuous function (440 words) [view diff] exact match in snippet view article find links to article

x ) = 1 {\displaystyle g(x)=1} whenever x {\displaystyle x} is an irrational number is nowhere quasi-continuous, since every nonempty open set G {\displaystyle

James A. Maynard (1,204 words) [view diff] case mismatch in snippet view article find links to article

Sloman, Leila (16 September 2019). "New Proof Solves 80-Year-Old Irrational Number Problem". Scientific American. Archived from the original on 24 May

Gelfond–Schneider constant (559 words) [view diff] exact match in snippet view article find links to article

623–634. Jarden, D. (1953), "Curiosa: A simple proof that a power of an irrational number to an irrational exponent may be rational", Scripta Mathematica, 19:

Existence theorem (631 words) [view diff] exact match in snippet view article find links to article

Geometrical proof that an irrational number exists: If the isosceles right triangle ABC had integer side lengths, so had the strictly smaller triangle

Pi Day (1,905 words) [view diff] case mismatch in snippet view article find links to article

Retrieved March 14, 2018. "Pi Day Turns 25: Why We Celebrate an Irrational Number". March 14, 2013. Archived from the original on March 14, 2013. Retrieved

Transcendental function (2,186 words) [view diff] exact match in snippet view article find links to article

the exponent π {\displaystyle \pi } can be replaced by any other irrational number, and the function will remain transcendental. For the second and third

1731 (1,660 words) [view diff] exact match in snippet view article find links to article

November 25 Swiss mathematician Leonhard Euler announces his use of the irrational number e (approximately 2.71828) as the base for the concept of the natural

Downsampling (signal processing) (1,804 words) [view diff] exact match in snippet view article

approach is applicable when the ratio Fy/Fx is a rational, or an irrational number, and is suitable for the sampling rate increase and for the sampling

Stanisław Świerczkowski (912 words) [view diff] exact match in snippet view article find links to article

theorem says: take arbitrarily finitely many integer multiples of an irrational number between zero and one and plot them as points around a circle of unit

Monotonic function (2,471 words) [view diff] exact match in snippet view article find links to article

{\displaystyle f(x)=\sum _{q_{i}\leq x}a_{i}} is continuous exactly at every irrational number (cf. picture). It is the cumulative distribution function of the discrete

Weyl sequence (305 words) [view diff] exact match in snippet view article find links to article

uniform distribution rather than a continuous one. Instead of using an irrational number, which cannot be calculated on a digital computer, the ratio of two

Terrence Howard (3,060 words) [view diff] exact match in snippet view article find links to article

Mathematics does not say that the square root of two is two, but an irrational number of approximately 1.41. Swartz, Tracy (November 23, 2015). "Terrence

Fractal sequence (539 words) [view diff] exact match in snippet view article find links to article

each h less than i occurs exactly once. Suppose θ is a positive irrational number. Let S(θ) = the set of numbers c + dθ, where c and d are positive

Locally compact space (2,522 words) [view diff] exact match in snippet view article find links to article

since any neighborhood contains a Cauchy sequence corresponding to an irrational number, which has no convergent subsequence in Q; the subspace { ( 0 , 0

Transfer principle (2,686 words) [view diff] exact match in snippet view article find links to article

represented by Q {\displaystyle \mathbb {Q} } . Thus, the notion of an irrational number is meaningless to even the most powerful floating-point computer.

Dimitris Koukoulopoulos (212 words) [view diff] case mismatch in snippet view article find links to article

Retrieved 2022-01-17. Sloman, Leila. "New Proof Solves 80-Year-Old Irrational Number Problem". Scientific American. Retrieved 2022-01-17. "ICM Number Theory

Numeral system (3,710 words) [view diff] exact match in snippet view article find links to article

base may repeat in another (thus 0.310 = 0.0100110011001...2). An irrational number stays aperiodic (with an infinite number of non-repeating digits)

The Books (1,957 words) [view diff] exact match in snippet view article find links to article

sampled brass and lyrics about the twelfth root of two (my favorite irrational number), trigonometry and tangrams". The album was released on July 20. The

Robert Smithson (3,151 words) [view diff] exact match in snippet view article find links to article

units, the title of which refers to the Greek word for an unnamable, irrational number. Smithson's interest in entropy led him to write about a future in

Zu Chongzhi (1,835 words) [view diff] case mismatch in snippet view article find links to article

ISBN 9780295963624. OCLC 17656687. Strogatz, Steven (2024-03-07). "Pi Day: How One Irrational Number Made Us Modern". The New York Times. ISSN 0362-4331. Retrieved 2024-03-15

List of circle topics (2,408 words) [view diff] exact match in snippet view article find links to article

Irrational rotation – Rotation of a circle by an angle of π times an irrational number Lens (geometry) – Convex plane region bounded by two circular arcs

Canons of page construction (2,443 words) [view diff] exact match in snippet view article find links to article

crucial relationship between short and long sides, and produces an irrational number, as pi is, but is a ratio of about 5:8 (footnote: The ratio is 0.618

Connected space (3,874 words) [view diff] exact match in snippet view article find links to article

{\displaystyle q_{1}<q_{2}} are in different components. Take an irrational number q 1 < r < q 2 , {\displaystyle q_{1}<r<q_{2},} and then set A = {

Kite (geometry) (3,800 words) [view diff] exact match in snippet view article

= 1 / φ 3 {\displaystyle \textstyle \alpha =1/\varphi ^{3}} ⁠, an irrational number, where ⁠ φ = 1 2 ( 1 + 5 ) {\displaystyle \varphi ={\tfrac {1}{2}}{\bigl

Richard Karpen (780 words) [view diff] case mismatch in snippet view article find links to article

Trombonist: The Conservation of Energy (2003) Solo/Tutti: Variations on an Irrational Number for amplified viola and real-time computer processing (2002) Aperture

Klein polyhedron (2,582 words) [view diff] exact match in snippet view article find links to article

^{n}} . Suppose α > 0 {\displaystyle \textstyle \alpha >0} is an irrational number. In R 2 {\displaystyle \textstyle \mathbb {R} ^{2}} , the cones generated

Infinite divisibility (1,935 words) [view diff] exact match in snippet view article find links to article

non-empty sets A and B where A contains all rationals less than some irrational number (π, say) and B all rationals greater than it, then A has no largest

Alice Duer Miller (2,664 words) [view diff] case mismatch in snippet view article find links to article

a student with her award-winning thesis "Dedekind's Theory of the Irrational Number". She and her sister Caroline jointly published a book of poems. Miller

Schanuel's conjecture (1,935 words) [view diff] exact match in snippet view article find links to article

e^{z_{2}w_{2}}.} The four exponential conjecture would imply that for any irrational number t {\displaystyle t} , at least one of the numbers 2 t {\displaystyle

Geometry (10,101 words) [view diff] case mismatch in snippet view article find links to article

(help) James R. Choike (1980). "The Pentagram and the Discovery of an Irrational Number". The Two-Year College Mathematics Journal. 11 (5): 312–316. doi:10

Generalized dihedral group (875 words) [view diff] exact match in snippet view article find links to article

Dih∞ as a 2-dimensional isometry group generated by a rotation by an irrational number of turns, and a reflection Both topological groups are totally disconnected

Restricted partial quotients (855 words) [view diff] exact match in snippet view article find links to article

{\overline {a_{k+1},a_{k+2},\dots ,a_{k+m}}}],\,} then ζ is a quadratic irrational number, and its representation as a regular continued fraction is periodic

Lebesgue integral (5,918 words) [view diff] exact match in snippet view article find links to article

subintervals, each partition contains at least one rational and at least one irrational number, because rationals and irrationals are both dense in the reals. Thus

Pythagorean theorem (12,692 words) [view diff] exact match in snippet view article find links to article

See James R. Choike (1980). "The pentagram and the discovery of an irrational number". The College Mathematics Journal. 11: 312–316. Kurt Von Fritz (Apr

Meantone temperament (3,959 words) [view diff] exact match in snippet view article find links to article

will never add up to a whole number of octaves, because log2 3 is an irrational number. If a stacked-up whole number of perfect fifths is too close to the

53 equal temperament (2,922 words) [view diff] exact match in snippet view article find links to article

"comma", however, is technically misleading, since this interval is an irrational number and it does not describe a compromise between intervals of any tuning

J-invariant (4,738 words) [view diff] exact match in snippet view article find links to article

Schneider proved the aforementioned result that if τ is a quadratic irrational number in the upper half plane then j(τ) is an algebraic integer. In addition

Kolmogorov–Arnold representation theorem (3,963 words) [view diff] exact match in snippet view article find links to article

1 ] 2 {\textstyle [0,1]^{2}} . Let t {\textstyle t} be a positive irrational number. Its exact value is irrelevant. We say that a 5-tuple ( ϕ 1 , … ,

Point groups in two dimensions (1,781 words) [view diff] exact match in snippet view article find links to article

\oplus } Z n generated by Cn and m independent rotations with an irrational number of turns, and m, n ≥ 1; for each pair (m, n) there are uncountably

List of Martin Gardner Mathematical Games columns (355 words) [view diff] exact match in snippet view article find links to article

Japanese art of folding objects out of paper 1959 Aug About phi, an irrational number that has some remarkable geometrical expressions 1959 Sep Concerning

Chinese mathematics (7,988 words) [view diff] exact match in snippet view article find links to article

years. He also applied He Chengtian's interpolation for approximating irrational number with fraction in his astronomy and mathematical works, he obtained

Equal temperament (7,383 words) [view diff] no match in snippet view article find links to article

explore systems that divide the octave into a non-integral (often irrational) number. In such temperaments, the interval between successive pitches is

Rounding (8,569 words) [view diff] exact match in snippet view article find links to article

problem Example input Result Rounding criterion Approximating an irrational number by a fraction π 22/7 1-digit-denominator Approximating a rational

Baker's theorem (3,418 words) [view diff] exact match in snippet view article find links to article

either a rational number or transcendental. It cannot be an algebraic irrational number like 2 {\displaystyle {\sqrt {2}}} . Although proving this result

Cyclic order (6,392 words) [view diff] exact match in snippet view article find links to article

called a gap. For example, the rational numbers Q have a gap at every irrational number. They also have a gap at infinity, i.e. the usual ordering. A cycle

Timeline of scientific discoveries (10,608 words) [view diff] case mismatch in snippet view article find links to article

Mathematics. James R. Choike (1980). "The Pentagram and the Discovery of an Irrational Number". The Two-Year College Mathematics Journal.. Warmflash, David (20

1730s (15,292 words) [view diff] exact match in snippet view article find links to article

November 25 Swiss mathematician Leonhard Euler announces his use of the irrational number e (approximately 2.71828) as the base for the concept of the natural

Tanguy Rivoal (481 words) [view diff] exact match in snippet view article find links to article

notable contributions include the proof that there is at least one irrational number among nine numbers ζ(5), ζ(7), ζ(9), ζ(11), ..., ζ(21), where ζ is

List of publications in mathematics (10,420 words) [view diff] exact match in snippet view article find links to article

as a finite continued fraction, that the continued fraction of an irrational number is infinite, and derived continued fraction expansions for e and e

Continued fraction (8,708 words) [view diff] exact match in snippet view article find links to article

continued fraction is roughly analogous to the construction of an irrational number as the limit of a Cauchy sequence of rational numbers. Because of

Radoslav Rochallyi (4,892 words) [view diff] exact match in snippet view article find links to article

University of Connecticut wrote that although the decimal expansion of any irrational number is infinite, the counting pattern in the poem uses only an approximation

Fourier amplitude sensitivity testing (3,603 words) [view diff] exact match in snippet view article find links to article

with all others being irrational. Since the numerical value of an irrational number cannot be stored exactly in a computer, an approximation of the incommensurate

Hajime Tanabe (8,722 words) [view diff] exact match in snippet view article find links to article

Parabolic space [放物線空間]; Elements at infinity [無窮遠要素]; Infinity [無限]; Irrational number [無理数]; Euclidean geometry [ユークリッド幾何学]; Rational number [有理数]; Dynamics/Mechanics

Cliquish function (464 words) [view diff] exact match in snippet view article find links to article

x ) = 1 {\displaystyle g(x)=1} whenever x {\displaystyle x} is an irrational number is nowhere cliquish, since every nonempty open set G {\displaystyle

List of compositions for viola: I to K (8,599 words) [view diff] case mismatch in snippet view article find links to article

viola and interactive electronics (2006) Solo/Tutti: Variations on an Irrational Number for amplified viola and real-time computer processing (2002) Laura

Pi is 3 (2,549 words) [view diff] exact match in snippet view article find links to article

treating pi as approximately 3 that were discussed, included "pi is an irrational number, so it is neither exactly 3 nor 3.14. Thus, while the former and the