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A point-to-line and line-to-point transformation which transforms points A into lines a^' and lines b into points B^' such that a^' passes through B^' iff A^' lies on b.

The pedal coordinates of a point P with respect to the curve C and the pedal point O are the radial distance r from O to P and the perpendicular distance p from O to the line ...

Given a point P, the point P^' which is the antipodal point of P is said to be the antipode of P. The term antipode is also used in plane geometry. Given a central conic (or ...

Every odd integer n is a prime or the sum of three primes. This problem is closely related to Vinogradov's theorem.

If the first case of Fermat's last theorem is false for the prime exponent p, then 3^(p-1)=1 (mod p^2).

A specific type of ultraproduct that can be used to construct nonstandard universes and obtain the transfer principle as a corollary of Łoś' theorem for ultraproducts.

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...

The definition of an Anosov map is the same as for an Anosov diffeomorphism except that instead of being a diffeomorphism, it is a map. In particular, an Anosov map is a C^1 ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...

The Yff circles are the two triplets of congruent circle in which each circle is tangent to two sides of a reference triangle. In each case, the triplets intersect pairwise ...