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In general, the word "complement" refers to that subset F^' of some set S which excludes a given subset F. Taking F and its complement F^' together then gives the whole of ...

The isogonal conjugate X^(-1) of a point X in the plane of the triangle DeltaABC is constructed by reflecting the lines AX, BX, and CX about the angle bisectors at A, B, and ...

The radical lines of three circles are concurrent in a point known as the radical center (also called the power center). This theorem was originally demonstrated by Monge ...

A Brocard line is a line from any of the vertices A_i of a triangle DeltaA_1A_2A_3 to the first Omega or second Omega^' Brocard point. Let the angle at a vertex A_i also be ...

Given a system of two ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y), (2) let x_0 and y_0 denote fixed points with x^.=y^.=0, so f(x_0,y_0) = 0 (3) g(x_0,y_0) ...

The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

There are at least two distinct notions of an intensity function related to the theory of point processes. In some literature, the intensity lambda of a point process N is ...

The mittenpunkt (also called the middlespoint) of a triangle DeltaABC is the symmedian point of the excentral triangle, i.e., the point of concurrence M of the lines from the ...