mathematics, a convex body in n {\displaystyle n} -dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a compact convex set with non-empty...

crescent shape, is not convex. The boundary of a convex set in the plane is always a convex curve. The intersection of all the convex sets that contain a...

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...

defined for any body (that is compact), but it is most useful for convex bodies (that is bodies, whose corresponding set is a convex set). The mean width...

authors have studied the computation of the volume of high-dimensional convex bodies, a problem that can also be used to model many other problems in combinatorial...

In mathematics, Minkowski's theorem is the statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to the...

in mathematical programming can be formulated as problems on convex sets or convex bodies. Six kinds of problems are particularly important:: Sec.2  optimization...

function constant inside a given convex body and vanishing outside; it corresponds to the uniform distribution on the convex body, which explains the term "central...

functions of several complex variables. Suppose K {\displaystyle K} is a convex, compact, and symmetric subset of R n {\displaystyle \mathbb {R} ^{n}} ...

Unsolved problem in mathematics Is there any three-dimensional convex body with lower packing density than the sphere? More unsolved problems in mathematics...

A convex cap, also known as a convex floating body or just floating body, is a well defined structure in mathematics commonly used in convex analysis for...

geometry asymptotic theory of convex bodies approximation by convex sets variants of convex sets (star-shaped, (m, n)-convex, etc.) Helly-type theorems and...

(combinatorial geometry) that for any n-dimensional convex body, at most 2n smaller homothetic bodies are necessary to contain the original Hadwiger's conjecture...

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...

dilations of some other convex body. A particular supply collection of interest is all Euclidean motions of a fixed convex body K. In this case, we call...

not other convex bodies; in fact Gritzmann and Arhelger observed that for any dimension d ≥ 3 {\displaystyle d\geq 3} there exists a convex shape for...

In mathematics, Minkowski's first inequality for convex bodies is a geometrical result due to the German mathematician Hermann Minkowski. The inequality...

Unsolved problem in mathematics Can every n {\displaystyle n} -dimensional convex body be covered by 2 n {\displaystyle 2^{n}} smaller copies of itself? More...

\Theta (n)} bits if defending against a strong opponent. The volume of a convex body can be estimated by a randomized algorithm to arbitrary precision in...

number of non-overlapping congruent copies of any convex body that touch a given copy of the body. There are different versions of the problem depending...

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...

more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to a tuple of convex bodies in R n {\displaystyle...

In algebraic geometry, a Newton–Okounkov body, also called an Okounkov body, is a convex body in Euclidean space associated to a divisor (or more generally...

In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular...

to the properties of convex bodies. A convex polyhedron is called a zonotope if it is the Minkowski sum of segments. A convex body which is a limit of...

literature on the convex hulls of Minkowski sumsets in its "Chapter 3 Minkowski addition" (pages 126–196): Schneider, Rolf (1993). Convex bodies: The Brunn–Minkowski...

surface area measure of a convex body in R n {\displaystyle \mathbb {R} ^{n}} . Here the surface area measure SK of a convex body K is the pushforward of...

generalized by May to the little convex bodies operad, and "little disks" is a case of "folklore" derived from the "little convex bodies". In graph theory, rooted...

{\displaystyle \epsilon >0} , we call a ϵ {\displaystyle \epsilon } -sphere a convex body K {\displaystyle K} such that there exists a ball B {\displaystyle B}...

In convex geometry, a zonoid is a type of centrally symmetric convex body. The zonoids have several definitions, equivalent up to translations of the resulting...