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It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...

Somos defines a rational triangle as a triangle such that all three sides measured relative to each other are rational. Koblitz (1993) defined a congruent number as an ...

The study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions. The ...

A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid. For a right pyramidal frustum, let s be the slant height, h the ...

A median A_1M_1 of a triangle DeltaA_1A_2A_3 is the Cevian from one of its vertices A_1 to the midpoint M_1 of the opposite side. The three medians of any triangle are ...

The word "median" has several different meanings in mathematics all related to the "middle" of mathematical objects. The statistical median is an order statistic that gives ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

In finding the average area A^__R of a triangle chosen from a closed, bounded, convex region R of the plane, then A^__(T(R))=A^__R, for T any nonsingular affine ...