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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 ...

The slant height of an object (such as a frustum, or pyramid) is the distance measured along a lateral face from the base to the apex along the "center" of the face. In other ...

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 ...

Let a Cevian PC be drawn on a triangle DeltaABC, and denote the lengths m=PA^_ and n=PB^_, with c=m+n. Then Stewart's theorem, also called Apollonius' theorem, states that ...

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 = ...

The center of the Taylor circle. It has triangle center function alpha_(389)=cosA-cos(2A)cos(B-C) and is Kimberling center X_(389), which is the center of the Spieker circle ...