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Any set of n+2 points in R^n can always be partitioned in two subsets V_1 and V_2 such that the convex hulls of V_1 and V_2 intersect.

The spherical curve obtained when moving along the surface of a sphere with constant speed, while maintaining a constant angular velocity with respect to a fixed diameter ...

Regular tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround each polygon vertex are called semiregular ...

Measurements of a centered convex body in Euclidean n-space (for n>=3) show that its brightness function (the volume of each projection) is smaller than that of another such ...

A four-sided quadrilateral not contained in a plane. The lines connecting the midpoints of opposite sides of a skew quadrilateral intersect (and bisect) each other (Steinhaus ...

A plane shape constructed by Reinhardt (1934) that is conjectured to be the "worst" packer of all centrally-symmetric plane regions. It has a packing density of ...

A closed three-dimensional figure (which may, according to some terminology conventions, be self-intersecting). Kern and Bland (1948, p. 18) define a solid as any limited ...

A spheric section is the curve formed by the intersection of a plane with a sphere. Excluding the degenerate cases of the plane tangent to the sphere or the plane not ...

A superegg is a solid described by the equation |sqrt((x^2+y^2)/(a^2))|^n+|z/b|^n=1. (1) The special case n=2 gives a spheroid. Special cases of volume V_n are given by V_1 = ...

Any nontrivial, closed, simple, smooth spherical curve dividing the surface of a sphere into two parts of equal areas has at least four inflection points.