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An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...

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 ...

The anticomplementary triangle is the triangle DeltaA_1^'A_2^'A_3^' which has a given triangle DeltaA_1A_2A_3 as its medial triangle. It is therefore the anticevian triangle ...

Also called Chvátal's art gallery theorem. If the walls of an art gallery are made up of n straight line segments, then the entire gallery can always be supervised by |_n/3_| ...

The Borromean rings, also called the Borromean links (Livingston 1993, p. 10) are three mutually interlocked rings (left figure), named after the Italian Renaissance family ...

The Brocard circle, also known as the seven-point circle, is the circle having the line segment connecting the circumcenter O and symmedian point K of a triangle DeltaABC as ...

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

The power of a fixed point A with respect to a circle of radius r and center O is defined by the product p=AP×AQ, (1) where P and Q are the intersections of a line through A ...

The theory of classifying problems based on how difficult they are to solve. A problem is assigned to the P-problem (polynomial-time) class if the number of steps needed to ...