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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 ...

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

Let P=alpha_1:beta_1:gamma_1 and Q=alpha_2:beta_2:gamma_2 be points, neither of which lie on a sideline of the reference triangle DeltaABC. The P-Ceva conjugate X of Q is ...

Three or more points P_1, P_2, P_3, ..., are said to be collinear if they lie on a single straight line L. A line on which points lie, especially if it is related to a ...

In the case of a general surface, the distance between two points measured along the surface is known as a geodesic. For example, the shortest distance between two points on ...

The term "wedge" has a number of different meanings in mathematics. It is sometimes used as another name for the caret symbol. The term also refers to the notation ( ^ ) used ...

Given a point with trilinear coordinates P=alpha:beta:gamma, the anticevian triangle DeltaA^'B^'C^' of a triangle DeltaABC with respect to P is a triangle such that 1. B^'C^' ...

The antipedal triangle DeltaA^'B^'C^' of a reference triangle DeltaABC with respect to a given point P is the triangle of which DeltaABC is the pedal triangle with respect to ...

Given a point P and a triangle DeltaABC, the Cevian triangle DeltaA^'B^'C^' is defined as the triangle composed of the endpoints of the cevians though the Cevian point P. A ...

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property ...