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The MacBeath inconic of a triangle is the inconic with parameters x:y:z=a^2cosA:b^2cosB:c^2cosC. (1) Its foci are the circumcenter O and the orthocenter H, giving the center ...

Consider Kimberling centers X_(20) (de Longchamps point Z; intersection L_S intersection L_E of the Soddy line and Euler line), X_(468) (intersection L_E intersection L_O of ...

Given a point P and a triangle DeltaABC, the Miquel triangle is the triangle DeltaP_AP_BP_C connecting the side points P_A, P_B, and P_C of DeltaABC with respect to which M ...

The catacaustic of a parabola (t,t^2) opening upward is complicated for a general radiant point (x,y). However, the equations simplify substantially in the case x=infty ...

Given n points, find the line segments with the shortest possible total length which connect the points. The segments need not necessarily be straight from one point to ...

The Thomson cubic Z(X_2) of a triangle DeltaABC is the locus the centers of circumconics whose normals at the vertices are concurrent. It is a self-isogonal cubic with pivot ...

The first de Villiers point is the perspector of the reference triangle and its BCI triangle, which is Kimberling center X_(1127) and has triangle center function ...

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...

Disconnectivities are mathematical entities which stand in the way of a space being contractible (i.e., shrunk to a point, where the shrinking takes place inside the space ...