In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas:...

In geometry, a set of points is convex if it contains every line segment between two points in the set. For example, a solid cube is a convex set, but...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is...

groups are sometimes regarded as strongly geometric as well. Convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues...

in the field of convex geometry. His first published article studied the combinatorial structures arising from intersections of convex polyhedra.[P85]...

solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic...

Discrete Geometry, Graduate Texts in Mathematics, vol. 212, Springer, ISBN 9780387953748, MR 1899299 Rockafellar, R. T. (1997) [1970]. Convex Analysis...

(disambiguation) Cone (geometry) Cone (topology) Farkas' lemma Bipolar theorem Ordered vector space Boyd, Stephen; Vandenberghe, Lieven (2004-03-08). Convex Optimization...

In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these...

In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points...

Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle...

Ziegler on the subject, as well as in many other texts in discrete geometry, convex polytopes are often simply called "polytopes". Grünbaum points out...

M. Gruber, Convex and discrete geometry, Springer-Verlag, New York, 2007. P. M. Gruber, J. M. Wills (editors), Handbook of convex geometry. Vol. A. B...

Still "Convex and abstract polytopes", Programme and abstracts, MIT, 2005 Johnson, Norman W. (2018). "§ 11.5 Spherical Coxeter groups". Geometries and Transformations...

Carathéodory's theorem in convex geometry states that if a point x {\displaystyle x} of R d {\displaystyle \mathbb {R} ^{d}} lies in the convex hull of a set P...

construct convex hulls of various objects have a broad range of applications in mathematics and computer science. In computational geometry, numerous...

Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex...

In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure...

In geometry, the tangent cone is a generalization of the notion of the tangent space to a manifold to the case of certain spaces with singularities. In...

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

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

In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that: Any set of d + 2 points in Rd can be partitioned into two...

Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial...

images Convex polygon Convex hull Smallest enclosing box "Rotating Calipers" at Toussaint's home page Shamos, Michael (1978). "Computational Geometry" (PDF)...

glossary. A caveat: many terms in Riemannian and metric geometry, such as convex function, convex set and others, do not have exactly the same meaning as...

In mathematics, specifically convex geometry, the normal fan of a convex polytope P is a polyhedral fan that is dual to P. Normal fans have applications...

2-dimensional geometry, a lens is a convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both...

of a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (some people use the term "circled" instead of...

Lithuanian-German, or Russian. He created and developed the geometry of numbers and elements of convex geometry, and used geometrical methods to solve problems in...