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At the points where a line X cuts the sides of a triangle DeltaA_1A_2A_3, draw three perpendiculars to the sides, one through each point of intersection. The resulting three ...

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 ...

In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number ...

Given triangle DeltaA_1A_2A_3, let the point of intersection of A_2Omega and A_3Omega^' be B_1, where Omega and Omega^' are the Brocard points, and similarly define B_2 and ...

A circumhyperbola is a circumconic that is a hyperbola. A rectangular circumhyperbola always passes through the orthocenter H and has center on the nine-point circle ...

The Clebsch diagonal cubic is a cubic algebraic surface given by the equation x_0^3+x_1^3+x_2^3+x_3^3+x_4^3=0, (1) with the added constraint x_0+x_1+x_2+x_3+x_4=0. (2) The ...

Chvátal defines the term hole to mean "a chordless cycle of length at least four." The restriction "of length at least four" allows use of the term "hole" regardless of if ...

If a points A^', B^', and C^' are marked on each side of a triangle DeltaABC, one on each side (or on a side's extension), then the three Miquel circles (each through a ...

A perpendicular bisector CD of a line segment AB is a line segment perpendicular to AB and passing through the midpoint M of AB (left figure). The perpendicular bisector of a ...

Perspective is the art and mathematics of realistically depicting three-dimensional objects in a two-dimensional plane, sometimes called centric or natural perspective to ...