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Take any triangle with polygon vertices A, B, and C. Pick a point A_1 on the side opposite A, and draw a line parallel to BC. Upon reaching the side AC at B_1, draw the line ...

f(I) is the collection of all real-valued continuous functions defined on some interval I. f^((n))(I) is the collection of all functions in f(I) with continuous nth ...

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 ...

Given any triangle ABC, the signed sum of perpendicular distances from the circumcenter O to the sides (i.e., signed lengths of the pedal lines from O) is OO_A+OO_B+OO_C=R+r, ...

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a ...

The de Longchamps point L is the reflection of the orthocenter H about the circumcenter O of a triangle. It has triangle center function alpha=cosA-cosBcosC, (1) and is ...

A transformation characterized by an invariant line and a scale factor (one-way stretch) or two invariant lines and corresponding scale factors (two-way stretch).

A Woo circle is an Archimedean circle with center on the Schoch line and tangent to certain other circles. An applet for investigating Woo circles and Schoch lines has been ...

A singular point of an algebraic curve is a point where the curve has "nasty" behavior such as a cusp or a point of self-intersection (when the underlying field K is taken as ...

While the pedal point, Cevian point, and even pedal-Cevian point are commonly used concepts in triangle geometry, there seems to be no established term to describe the ...