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p^x is an infinitary divisor of p^y (with y>0) if p^x|_(y-1)p^y, where d|_kn denotes a k-ary Divisor (Guy 1994, p. 54). Infinitary divisors therefore generalize the concept ...

The Johnson graph J(n,k) has vertices given by the k-subsets of {1,...,n}, with two vertices connected iff their intersection has size k-1. Special classes are summarized in ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

The lines containing the three points of the intersection of the three pairs of opposite sides of a (not necessarily regular) hexagon. There are 6! (i.e., 6 factorial) ...

P is the point on the line AB such that PA^_/PB^_=1. It can also be thought of as the point of intersection of two parallel lines. In 1639, Desargues (1864) became the first ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

Sangaku problems, often written "san gaku," are geometric problems of the type found on devotional mathematical wooden tablets ("sangaku") which were hung under the roofs of ...

A list of five properties of a topological space X expressing how rich the "population" of open sets is. More precisely, each of them tells us how tightly a closed subset can ...

From the feet H_A, H_B, and H_C of each altitude of a triangle DeltaABC, draw lines (H_AP_A,H_AQ_A), (H_BP_B,H_BQ_B), (H_CP_C,H_CQ_C) perpendicular to the adjacent sides, as ...