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The outer Vecten circle is the circumcircle of the outer Vecten triangle. It has center at Kimberling center X_(641), which is the complement of the outer Vecten point ...

A skew polygon such that every two consecutive sides (but no three) belong to a face of a regular polyhedron. Every regular polyhedron can be orthogonally projected onto a ...

Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Poincaré inequality ...

The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...

The second Morley adjunct triangle has trilinear vertex matrix [2 sec[1/3(C-2pi)] sec[1/3(B-2pi)]; sec[1/3(C-2pi)] 2 sec[1/3(A-2pi)]; sec[1/3(B-2pi)] sec[1/3(A-2pi)] 2]. The ...

Given 2n-1 numbers a_k, where k=-n+1, ..., -1, 0, 1, ..., n-1, a Toeplitz matrix is a matrix which has constant values along negative-sloping diagonals, i.e., a matrix of the ...

The exact values of cos(pi/18) and sin(pi/18) can be given by infinite nested radicals sin(pi/(18))=1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2-...)))), where the sequence of signs +, +, ...

An invariant of an elliptic curve given in the form y^2=x^3+ax+b which is closely related to the elliptic discriminant and defined by j(E)=(2^83^3a^3)/(4a^3+27b^2). The ...

The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński ...

Klee's identity is the binomial sum sum_(k=0)^n(-1)^k(n; k)(n+k; m)=(-1)^n(n; m-n), where (n; k) is a binomial coefficient. For m=0, 1, ... and n=0, 1,..., the following ...