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Let P=p:q:r and U=u:v:w be points in trilinear coordinates, neither of which is on a side line of a reference triangle DeltaABC. Them the P-isoconjugate of U is the point ...

Suppose a line L^' meets sidelines BC, CA, and AB in points A^', B^', and C^', respectively. Let A^('') be the reflection of A^' about the midpoint of segment BC, and ...

The Lemoine cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=3, 4, 32, 56, and 1147.

A point about which inversion of two circles produced concentric circles. Every pair of distinct circles has two limiting points. The limiting points correspond to the point ...

Given a triangle DeltaABC, construct the contact triangle DeltaDEF. Then the Nobbs points are the intersections of the corresponding sides of triangles DeltaABC and DeltaDEF, ...

The orthic inconic of a triangle is the inconic with inconic parameters x:y:z=cosA:cosB:cosC. (1) It has trilinear equation ...

The outer Soddy circle is the solution to the four coins problem. It has circle function l=((-a+b+c)^2[f(a,b,c)+16g(a,b,c)rs])/(4bc[(a^2+b^2+c^2)-2(ab+bc+ca)+8rs]^4), (1) ...

If P(z) is a power series which is regular for |z|<=1 except for m poles within this circle and except for z=+1, at which points the function is assumed continuous when only ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

The Patterson graph is the graph whose vertices are the 22880 centers of the Sylow 3-groups of the Suzuki group and in which two vertices are adjacent whenever they generate ...