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Bernstein's problem
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differential geometry, Bernstein's problem is as follows: if the graph of a function on Rn−1 is a minimal surface in Rn, does this imply that the functionQuadratrix of Hippias (3,235 words) [view diff] exact match in snippet view article find links to article
Quadratrix as the graph of a function for a = 1 {\displaystyle a=1}Correspondence (algebraic geometry) (293 words) [view diff] exact match in snippet view article
The typical example of the latter kind of correspondence is the graph of a function f:X→Y. Correspondences also play an important role in the constructionDecision problem (1,246 words) [view diff] exact match in snippet view article find links to article
decision problem is just the graph of the associated function. (The graph of a function f is the set of pairs (x,y) such that f(x) = y.) If this decisionSine and cosine (7,064 words) [view diff] no match in snippet view article find links to article
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle:Implicit surface (2,423 words) [view diff] exact match in snippet view article find links to article
Implicit means that the equation is not solved for x or y or z. The graph of a function is usually described by an equation z = f ( x , y ) {\displaystyleGaussian curvature (2,669 words) [view diff] exact match in snippet view article find links to article
We represent the surface by the implicit function theorem as the graph of a function, f, of two variables, in such a way that the point p is a criticalMaxima (software) (1,160 words) [view diff] exact match in snippet view article
Maxima Screenshot of Maxima, plotting the 2D graph of a function with the gnuplot-x11 package running on Ubuntu Linux Developer(s) Macsyma group at ProjectLimit of a function (11,342 words) [view diff] exact match in snippet view article find links to article
this is the limiting value of the slope of secant lines to the graph of a function. Although implicit in the development of calculus of the 17th andInjective function (2,589 words) [view diff] exact match in snippet view article find links to article
embedding. Unlike surjectivity, which is a relation between the graph of a function and its codomain, injectivity is a property of the graph of the functionKleene's recursion theorem (3,095 words) [view diff] exact match in snippet view article find links to article
if the fixed point F is not the graph of a function, then there is some k such that Fk is not the graph of a function. Compared to the second recursionHermitian adjoint (3,270 words) [view diff] exact match in snippet view article find links to article
H\oplus H} of the graph G ( A ) {\displaystyle G(A)} is the graph of a function. Since G cl ( A ) {\displaystyle G^{\text{cl}}(A)} is a (closed)Pullback (category theory) (2,061 words) [view diff] exact match in snippet view article
binary product). A specific example of a pullback is given by the graph of a function. Suppose that f : X → Y {\displaystyle f\colon X\to Y} is a functionWeierstrass function (2,430 words) [view diff] exact match in snippet view article find links to article
we try to draw a general continuous function, we usually draw the graph of a function which is Lipschitz or otherwise well-behaved. Moreover, the factQuasiconvex function (1,451 words) [view diff] exact match in snippet view article find links to article
The graph of a function that is both concave and quasiconvex on the nonnegative real numbers.Henri Lebesgue (2,242 words) [view diff] exact match in snippet view article find links to article
that corresponds to the informal idea of finding the area under the graph of a function. The first theory of integration was developed by Archimedes in theAbsoluteness (logic) (1,260 words) [view diff] no match in snippet view article
successor ordinal. x is a limit ordinal. x = ω. x is finite. x is (the graph of) a function. Other properties are not absolute: being countable being a cardinalNormal (geometry) (2,640 words) [view diff] exact match in snippet view article
{\displaystyle S} in R 3 {\displaystyle \mathbb {R} ^{3}} given as the graph of a function z = f ( x , y ) , {\displaystyle z=f(x,y),} an upward-pointing normalSergei Adian (905 words) [view diff] exact match in snippet view article find links to article
students. In his first work as a student in 1950, Adian proved that the graph of a function f ( x ) {\displaystyle f(x)} of a real variable satisfying the functionalAlgebraic curve (7,993 words) [view diff] exact match in snippet view article find links to article
implicit equation of the curve, in contrast to the curves that are the graph of a function defining explicitly y as a function of x. With a curve given by suchFive points determine a conic (2,331 words) [view diff] exact match in snippet view article find links to article
in the plane, and the intersections of corresponding lines to the graph of a function, which (must be shown) is a hyperbola, hence a conic, hence the originalCycloid (3,936 words) [view diff] exact match in snippet view article find links to article
{\displaystyle 0\leq x\leq 2\pi } . Considering the cycloid as the graph of a function y = f ( x ) {\displaystyle y=f(x)} , it satisfies the differentialHyperbola (13,603 words) [view diff] exact match in snippet view article find links to article
={\tfrac {a^{2}/2}{\xi }}\ .} Thus, in an xy-coordinate system the graph of a function f : x ↦ A x , A > 0 , {\displaystyle f:x\mapsto {\tfrac {A}{x}},\;A>0\;Hunting oscillation (4,087 words) [view diff] exact match in snippet view article find links to article
track and the wheel pair is centered on the track. See Curvature#Graph of a function for mathematical details. The approximate equality becomes equalityGlossary of mathematical jargon (5,467 words) [view diff] exact match in snippet view article find links to article
\mathbb {R} ,(x,y)\mapsto x} is a projection and its restriction to a graph of a function, say, is also a projection. The terms “idempotent operator” and “forgetfulPi (17,241 words) [view diff] exact match in snippet view article find links to article
For example, an idealized vibrating string can be modelled as the graph of a function f on the unit interval [0, 1], with fixed ends f(0) = f(1) = 0. ThePólya–Szegő inequality (2,247 words) [view diff] exact match in snippet view article find links to article
cylinders and an asymptotics expansion of the area of the area of the graph of a function. The inequality is proved for a smooth function u {\displaystyleWeierstrass transform (2,865 words) [view diff] exact match in snippet view article find links to article
The graph of a function f ( x ) {\displaystyle f(x)} (black) and its generalized Weierstrass transforms for five t {\displaystyle t} parameters. The standardConstructive set theory (35,229 words) [view diff] exact match in snippet view article find links to article
set theoretical notion here, one may explicitly call the latter graph of a function, anafunction or set function. The axiom schema of Replacement can