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The third Morley triangle is made by rotating line BC toward vertex A about vertex B by angle (B+4pi)/3. It is an equilateral triangle. It has trilinear vertex matrix [1 ...

A leg of a right triangle (i.e., a side adjacent the right angle) is also known as a cathetus (plural: catheti). While this usage is rather rare in English, the terms ...

A beautiful general theorem of which the following two statements are special cases (Coxeter and Greitzer 1967, pp. 99-100). 1. If DeltaABC and DeltaA^'B^'C^' are two ...

Ball triangle picking is the selection of triples of points (corresponding to vertices of a general triangle) randomly placed inside a ball. n random triangles can be picked ...

The cyclocevian triangle DeltaA^('')B^('')C^('') of a reference triangle DeltaABC with respect to a point P is the triangle formed by the vertices determined by the ...

The vertex triangle of two distinct circumcevian triangles or circumanticevian triangles is perspective to the reference triangle. In addition, the vertex triangles of the ...

The circumnormal triangle is an equilateral triangle with vertices on the circumcircle of a reference triangle DeltaABC obtained by rotating the circumtangential triangle by ...

The circumtangential triangle is an equilateral triangle formed by the three points X on the circumcircle of a reference triangle DeltaABC at which the line XX^(-1), where ...

A polygonal diagonal is a line segment connecting two nonadjacent polygon vertices of a polygon. The number of ways a fixed convex n-gon can be divided into triangles by ...

The numerators and denominators obtained by taking the ratios of adjacent terms in the triangular array of the number of +1 "bordered" alternating sign matrices A_n with a 1 ...