Search results

Several theorems are named after [[Augustin-Louis Cauchy]]. '''Cauchy theorem''' may mean: *[[Cauchy's integral theorem]] in complex analysis, also [[Cauchy's integral formula]] ...

{{Short description|Theorem in integral geometry}} ...s the [[Valuation (geometry)|valuations]] on [[Convex body|convex bodies]] in <math>\R^n.</math> It was proved by [[Hugo Hadwiger]]. ...

{{Short description|Branch of geometry}} {{about|the study of convex sets|the combinatorial set systems|antimatroid}} ...

...is is a convex combination of two colors allowing for transparency effects in computer graphics. ...placed at its vertices. The coordinates are non-negative for points in the convex hull. ...

{{Short description|Concept in geometry}} ...by the two [[ray (geometry)|rays]] between the vertex and each [[endpoint (geometry)|endpoint]] of the segment. ...

{{short description|Gives the average curvature of any closed convex plane curve}} {{About|the concept in geometry|the concept in [[mathematical optimization]]|Fenchel's duality theorem}} ...

{{short description|Theorem about the intersections of d-dimensional convex sets}} ...em.svg|thumb|400px|Helly's theorem for the Euclidean plane: if a family of convex sets has a nonempty intersection for every triple of sets, then the whole f ...

{{short description|One of several theorems in different areas of mathematics}} ...ry]], '''Schur's theorem''' is a theorem of [[:de:Axel Schur|Axel Schur]]. In [[functional analysis]], '''Schur's theorem''' is often called [[Schur's pr ...

In [[geometry]], '''Barbier's theorem''' states that every [[curve of constant width]] h | title = Convex Sets and Their Applications ...

...points.svg|thumb|right|A convex set in light blue, and its extreme points in red.]] ...lems|title=What is the difference between corner points and extreme points in linear programming problems?|last=Saltzman|first=Matthew}}</ref> ...

{{short description|On partitions into intersecting convex hulls}} ...he vertices of a regular [[heptagon]] into three subsets with intersecting convex hulls.]] ...

...[Hyperbolic triangle|hyperbolic]]; that is, the middle one in the picture. In fact, any complete metric space where a triangle is hyperbolic is an Hadama ...Jacques Hadamard]], is a non-linear generalization of a [[Hilbert space]]. In the literature they are also equivalently defined as complete [[CAT(k) spac ...

...the convex hull of a set P in Rd, is the convex combination of d+1 points in P}} ...math>P</math> without changing the membership of ''<math>x</math>'' in the convex hull. ...

{{short description|Theorem in hyperbolic geometry}} In [[hyperbolic geometry]], two lines are said to be '''ultraparallel''' if they do not intersect an ...

...[[area]] of any convex [[cyclic quadrilateral]] (one that can be inscribed in a circle) given the lengths of the sides. Its generalized version, ''[[Bret Brahmagupta's formula gives the area {{math|''K''}} of a convex [[cyclic quadrilateral]] whose sides have lengths {{math|''a''}}, {{math|'' ...

{{Short description|Theorem in plane geometry}} ...Aubel|Henricus Hubertus (Henri) Van Aubel]] (1830–1906), who published it in 1878.<ref>{{citation|last=Van Aubel|first=H.|language=French|title=Note con ...

...wer]] minimal surface. [[Minimal surface]]s are among the objects of study in geometric analysis.]] ...al equation]]s (PDEs), are used to establish new results in [[differential geometry]] and [[differential topology]]. The use of [[linear differential equation| ...

...it into a finite number of pieces and recomposing these by [[Translation (geometry)|translations]] and [[rotation]]s. The Wallace–Bolyai–Gerwien theorem state ...lliam Wallace (mathematician)|Wallace]] had proven the same result already in 1807. ...

In [[mathematics]], the '''Weinstein conjecture''' refers to a general existen ...Since, as is trivial to show, any orbit of a Hamiltonian flow is contained in a level set, the Weinstein conjecture is a statement about contact manifold ...

...ription|On the area enclosed by a point on a rigid chord rotating inside a convex closed curve}} ...at of the original curve by <math>\pi pq</math>. The theorem was published in 1858 by Rev. [[Hamnet Holditch]].<ref name=Pickover/><ref>{{citation|last=H ...