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The MacBeath inconic of a triangle is the inconic with parameters x:y:z=a^2cosA:b^2cosB:c^2cosC. (1) Its foci are the circumcenter O and the orthocenter H, giving the center ...

The intersection Ev of the Gergonne line and the Euler line. It has triangle center function alpha=(b(a-b+c)cosB+c(a+b-c)cosC-2a^2cosA)/(2a) and is Kimberling center X_(1375).

The Napoleon crossdifference is the crossdifference of the Napoleon points. It has triangle center function alpha_(1510)=((b^2-c^2)[2cos(2A)-1])/a and is Kimberling center ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...

The first de Villiers point is the perspector of the reference triangle and its BCI triangle, which is Kimberling center X_(1127) and has triangle center function ...

The conjecture due to Pollock (1850) that every number is the sum of at most five tetrahedral numbers (Dickson 2005, p. 23; incorrectly described as "pyramidal numbers" and ...

A face-centered cubic sphere packing obtained by placing layers of spheres one on top of another. Because there are two distinct ways to place each layer on top of the ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

A 32-sided polygon. The regular icosidodecagon is a constructible polygon, and the regular icosidodecahedron of side length 1 has inradius r, circumradius R, and area A r = ...

A hendecagon is an 11-sided polygon, also variously known as an undecagon or unidecagon. The term "hendecagon" is preferable to the other two since it uses the Greek prefix ...