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The second de Villiers point is the perspector of the reference triangle and the excenter analog of the BCI triangle, which is Kimberling center X_(1128) has triangle center ...

Two points P,Q on a compact Riemann surface such that P lies on every geodesic passing through Q, and conversely. An oriented surface where every point belongs to a ...

Given a triangle with one vertex at the origin and the others at positions v_1 and v_2, one might think that a random point inside the triangle would be given by ...

An incidence system (v, k, lambda, r, b) in which a set X of v points is partitioned into a family A of b subsets (blocks) in such a way that any two points determine lambda ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

There are three theorems related to pedal circles that go under the collective title of the Fontené theorems. The first Fontené theorem lets DeltaABC be a triangle and P an ...

In the plane, the reflection property can be stated as three theorems (Ogilvy 1990, pp. 73-77): 1. The locus of the center of a variable circle, tangent to a fixed circle and ...

The discrete Fourier transform of length N (where N is even) can be rewritten as the sum of two discrete Fourier transforms, each of length N/2. One is formed from the ...

Fano's geometry is a finite geometry attributed to Fano from around the year 1892. This geometry comes with five axioms, namely: 1. There exists at least one line. 2. Every ...

The theorem of Möbius tetrads, also simply called Möbius's theorem by Baker (1925, p. 18), may be stated as follows. Let P_1, P_2, P_3, and P_4 be four arbitrary points in a ...