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searching for Convex geometry 47 found (153 total)

M. Riesz extension theorem (1,276 words) [view diff] no match in snippet view article find links to article

The M. Riesz extension theorem is a theorem in mathematics, proved by Marcel Riesz during his study of the problem of moments. Let E {\displaystyle E}

Alexandrov's uniqueness theorem (1,734 words) [view diff] no match in snippet view article find links to article

The Alexandrov uniqueness theorem is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between

Kakutani fixed-point theorem (3,237 words) [view diff] no match in snippet view article find links to article

In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set-valued

Helly's theorem (958 words) [view diff] case mismatch in snippet view article find links to article

(1993), "Helly, Radon, and Carathéodory type theorems", Handbook of Convex Geometry, vol. A, B, Amsterdam: North-Holland, pp. 389–448. Heinrich Guggenheimer

Cauchy's theorem (geometry) (768 words) [view diff] case mismatch in snippet view article

Comm. Pure Appl. Math. 21 (1968), 119–168. Robert Connelly, "Rigidity", in Handbook of Convex Geometry, vol. A, 223–271, North-Holland, Amsterdam, 1993.

Newton–Okounkov body (333 words) [view diff] exact match in snippet view article find links to article

to a divisor (or more generally a linear system) on a variety. The convex geometry of a Newton–Okounkov body encodes (asymptotic) information about the

Hadwiger's theorem (519 words) [view diff] no match in snippet view article find links to article

In integral geometry (otherwise called geometric probability theory), Hadwiger's theorem characterises the valuations on convex bodies in R n . {\displaystyle

Geoffrey Colin Shephard (218 words) [view diff] exact match in snippet view article find links to article

August 1927 - 3 August 2016) was a British mathematician who worked on convex geometry and reflection groups. He asked Shephard's problem on the volumes of

Kakutani's theorem (geometry) (133 words) [view diff] no match in snippet view article

Kakutani's theorem is a result in geometry named after Shizuo Kakutani. It states that every convex body in 3-dimensional space has a circumscribed cube

Busemann's theorem (193 words) [view diff] no match in snippet view article find links to article

In mathematics, Busemann's theorem is a theorem in Euclidean geometry and geometric tomography. It was first proved by Herbert Busemann in 1949 and was

Radon's theorem (2,424 words) [view diff] case mismatch in snippet view article find links to article

(1993), "Helly, Radon, and Carathéodory type theorems", Handbook of Convex Geometry, vol. A, B, Amsterdam: North-Holland, pp. 389–448. Kay, David C.; Womble

Tverberg's theorem (1,339 words) [view diff] no match in snippet view article find links to article

In discrete geometry, Tverberg's theorem, first stated by Helge Tverberg in 1966, is the result that sufficiently many points in Euclidean space can be

Kirchberger's theorem (902 words) [view diff] exact match in snippet view article find links to article

Raphael (2020), "Topological drawings meet classical theorems from convex geometry", Proceedings of the 28th International Symposium on Graph Drawing

Constantin Carathéodory (4,926 words) [view diff] exact match in snippet view article find links to article

optimal control and dynamic programming. Carathéodory's theorem in convex geometry states that if a point x {\displaystyle x} of R d {\displaystyle \mathbb

Back-face culling (1,400 words) [view diff] exact match in snippet view article find links to article

partially address the problem of hidden-line removal, but only for closed convex geometry. Back-face culling can also be applied to flat surfaces other than

Toric variety (2,259 words) [view diff] exact match in snippet view article find links to article

polytope, which creates a powerful connection of the subject with convex geometry. Familiar examples of toric varieties are affine space, projective

Brunn–Minkowski theorem (2,993 words) [view diff] exact match in snippet view article find links to article

of mass can be much larger than r(x). Sometimes in the context of a convex geometry, the radius function has a different meaning, here we follow the terminology

Brouwer fixed-point theorem (8,424 words) [view diff] no match in snippet view article find links to article

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f

András Prékopa (1,431 words) [view diff] exact match in snippet view article find links to article

programming, as they found applications in physics, economics, statistics, convex geometry and other fields. He received his university diploma as teacher of

Tommy Bonnesen (402 words) [view diff] exact match in snippet view article find links to article

his death. Tommy Bonnesen is internationally known for his work in convex geometry, and a generalization of the isoperimetric inequality, which establishes

Block graph (985 words) [view diff] exact match in snippet view article find links to article

the connected subsets of vertices in a connected block graph form a convex geometry, a property that is not true of any graphs that are not block graphs

Claude Ambrose Rogers (463 words) [view diff] case mismatch in snippet view article find links to article

Topology of Banach Spaces, Selection Theorems and Finite-dimensional Convex Geometry. In the theory of Banach spaces and summability, he proved the Dvoretzky–Rogers

Bernd Sturmfels (362 words) [view diff] case mismatch in snippet view article find links to article

Mathematics in the Sciences Thesis Oriented Matroids and Combinatorial Convex Geometry; Computational Synthetic Geometry Doctoral advisor Jürgen Bokowski

Catalan solid (481 words) [view diff] case mismatch in snippet view article find links to article

convex bodies", in Gruber, P. M.; Wills, J. M. (eds.), Handbook of Convex Geometry, North Holland, ISBN 978-0-08-093439-6 Wenninger, Magnus (1983), Dual

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

usually mentioned in any good reference on convex geometry, for instance, Selected topics in convex geometry by Maria Moszyńska (Birkhäuser, Boston 2006)

Geometry of numbers (1,054 words) [view diff] exact match in snippet view article find links to article

New York, 2007. P. M. Gruber, J. M. Wills (editors), Handbook of convex geometry. Vol. A. B, North-Holland, Amsterdam, 1993. M. Grötschel, Lovász, L

Flexible polyhedron (920 words) [view diff] exact match in snippet view article find links to article

ISBN 978-1-4684-6688-1. Connelly, Robert (1993), "Rigidity" (PDF), Handbook of convex geometry, Vol. A, B, Amsterdam: North-Holland, pp. 223–271, MR 1242981. Demaine

Peter McMullen (755 words) [view diff] exact match in snippet view article find links to article

as "Valuations and dissections" (by McMullen alone) in Handbook of convex geometry (1993), MR1243000. Books ——; Shephard, Geoffrey C. (1971), Convex Polytopes

Barbier's theorem (669 words) [view diff] case mismatch in snippet view article find links to article

Constant Brightness", Bodies of Constant Width: An Introduction to Convex Geometry with Applications, Birkhäuser, pp. 310–313, doi:10.1007/978-3-030-03868-7

Jean Bourgain (1,523 words) [view diff] exact match in snippet view article find links to article

what became known as the Bourgain slicing problem in high-dimensional convex geometry. In 1985, he proved Bourgain's embedding theorem in metric dimension

László Fejes Tóth (2,552 words) [view diff] exact match in snippet view article find links to article

Tóth with several influential proofs in the field of discrete and convex geometry, pertaining to packings and coverings by circles, to convex sets in

Generalized conic (3,000 words) [view diff] case mismatch in snippet view article find links to article

on generalized conics in the book Convex Geometry by Csaba Vincze available online. Csaba Vincze. "Convex Geometry Chapter 10. Generalized Conics". Digitalis

Alfréd Rényi Institute of Mathematics (521 words) [view diff] case mismatch in snippet view article find links to article

Research Council research group, head: Endre Szemerédi) Discrete and Convex Geometry (European Research Council research group, head: Imre Bárány) Didactics

Reuleaux polygon (669 words) [view diff] case mismatch in snippet view article find links to article

1: Reuleaux Polygons", Bodies of Constant Width: An Introduction to Convex Geometry with Applications, Birkhäuser, pp. 167–169, doi:10.1007/978-3-030-03868-7

Igor Rivin (840 words) [view diff] exact match in snippet view article find links to article

inscribable combinatorial types. These, and some related results in convex geometry, have been used in 3-manifold topology, theoretical physics, computational

Ilona Palásti (717 words) [view diff] exact match in snippet view article find links to article

MR 1469759. See in particular p. 205. Bárány, Imre (2006), "Discrete and convex geometry", in Horváth, János (ed.), A panorama of Hungarian mathematics in the

Ptolemaic graph (808 words) [view diff] exact match in snippet view article find links to article

contain every shortest path between two vertices in the subset) form a convex geometry. That is, every convex set can be reached from the whole vertex set

Cone of curves (1,007 words) [view diff] exact match in snippet view article find links to article

X ) {\displaystyle NE(X)} is indeed a convex cone in the sense of convex geometry. One useful application of the notion of the cone of curves is the

Blaschke–Lebesgue theorem (1,106 words) [view diff] exact match in snippet view article find links to article

Oliveros, Déborah (2019), Bodies of Constant Width: An introduction to convex geometry with applications, Birkhäuser/Springer, Cham, p. 336, doi:10.1007/978-3-030-03868-7

Funk transform (1,195 words) [view diff] exact match in snippet view article find links to article

introduced by Tuch (2004). It is also related to intersection bodies in convex geometry. Let K ⊂ R d {\displaystyle K\subset \mathbb {R} ^{d}} be a star body

Graduate Texts in Mathematics (5,035 words) [view diff] case mismatch in snippet view article find links to article

Space, Konrad Schmüdgen (2020, ISBN 978-3-030-46365-6) Lectures on Convex Geometry, Daniel Hug, Wolfgang Weil (2020, ISBN 978-3-030-50179-2) Explorations

Tropical geometry (3,632 words) [view diff] case mismatch in snippet view article find links to article

S2CID 155827635. This is a digest of Y. Shiozawa, "Subtropical Convex Geometry as the Ricardian Theory of International Trade" draft paper. Zhang

Curve of constant width (3,608 words) [view diff] case mismatch in snippet view article find links to article

Oliveros, Déborah (2019). Bodies of Constant Width: An Introduction to Convex Geometry with Applications. Birkhäuser. doi:10.1007/978-3-030-03868-7. ISBN 978-3-030-03866-3

Pi (17,248 words) [view diff] case mismatch in snippet view article find links to article

Oliveros, Déborah (2019). Bodies of Constant Width: An Introduction to Convex Geometry with Applications. Birkhäuser. doi:10.1007/978-3-030-03868-7. ISBN 978-3-030-03866-3

Oriented matroid (3,970 words) [view diff] exact match in snippet view article find links to article

In convex geometry, the simplex algorithm for linear programming is interpreted as tracing a path along the vertices of a convex polyhedron. Oriented

List of women in mathematics (23,253 words) [view diff] exact match in snippet view article find links to article

Shiri Artstein (born 1978), Israeli mathematician specializing in convex geometry and asymptotic geometric analysis Marcia Ascher (1935–2013), American

Reuleaux triangle (6,497 words) [view diff] case mismatch in snippet view article find links to article

Oliveros, Déborah (2019), Bodies of Constant Width: An Introduction to Convex Geometry with Applications, Birkhäuser, p. 3, doi:10.1007/978-3-030-03868-7