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The second Napoleon point N^', also called the inner Napoleon point, is the concurrence of lines drawn between polygon vertices of a given triangle DeltaABC and the opposite ...

Let X be a locally convex topological vector space and let K be a compact subset of X. In functional analysis, Milman's theorem is a result which says that if the closed ...

A number of attractive 12-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

If F is a family of more than n bounded closed convex sets in Euclidean n-space R^n, and if every H_n (where H_n is the Helly number) members of F have at least one point in ...

The regular heptagon is the seven-sided regular polygon illustrated above, which has Schläfli symbol {7}. According to Bankoff and Garfunkel (1973), "since the earliest days ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

The nonagon, also known as an enneagon, is a 9-sided polygon. Although the term "enneagon" is perhaps preferable (since it uses the Greek prefix and suffix instead of the ...

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 ...

Let A be a closed convex subset of a Banach space and assume there exists a continuous map T sending A to a countably compact subset T(A) of A. Then T has fixed points.

A convex polyhedron is defined as the set of solutions to a system of linear inequalities mx<=b (i.e., a matrix inequality), where m is a real s×d matrix and b is a real ...