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Given positive numbers s_a, s_b, and s_c, the Elkies point is the unique point Y in the interior of a triangle DeltaABC such that the respective inradii r_a, r_b, r_c of the ...

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 point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...

If f is analytic on a domain U, then a point z_0 on the boundary partialU is called regular if f extends to be an analytic function on an open set containing U and also the ...

A singular point such that every neighborhood of the point intersects itself. Pinch points are also called Whitney singularities or branch points.

Let DeltaA^'B^'C^' be the reflection of the orthic triangle of the reference triangle DeltaABC in the nine-point center. Then DeltaA^'B^'C^' and DeltaABC are in perspective, ...

The Gergonne point Ge is the perspector of a triangle DeltaABC and its contact triangle DeltaT_AT_BT_C. It has equivalent triangle center functions alpha = [a(b+c-a)]^(-1) ...

The point of concurrence of the six planes in Monge's tetrahedron theorem.

A point at which two noncrossing branches of a curve meet with different tangents.

A point p on a regular surface M in R^3 is said to be elliptic if the Gaussian curvature K(p)>0 or equivalently, the principal curvatures kappa_1 and kappa_2 have the same ...