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A figurate number corresponding to a pentagonal pyramid. The first few are 1, 6, 18, 40, 75, ... (OEIS A002411). The generating function for the pentagonal pyramidal numbers ...

A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

SNTP(n) is the smallest prime such that p#-1, p#, or p#+1 is divisible by n, where p# is the primorial of p. Ashbacher (1996) shows that SNTP(n) only exists 1. If there are ...

The maximal number of regions into which space can be divided by n planes is f(n)=1/6(n^3+5n+6) (Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ..., these give the values ...

The third Brocard point has triangle center function alpha=a^(-3) and is Kimberling center X_(76) (Kimberling 1998, p. 78). The point may have received its name since its ...

The Thomson cubic Z(X_2) of a triangle DeltaABC is the locus the centers of circumconics whose normals at the vertices are concurrent. It is a self-isogonal cubic with pivot ...

With n cuts of a torus of genus 1, the maximum number of pieces which can be obtained is N(n)=1/6(n^3+3n^2+8n). The first few terms are 2, 6, 13, 24, 40, 62, 91, 128, 174, ...

A circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are the Mohammed sign and unicursal hexagram. The numbers of ...

A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

Weill's theorem states that, given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, ...