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The triangle space T is the set of triples (a,b,c) of real numbers that are side lengths of a (Euclidean) triangle, i.e., T={(a,b,c):0<a<b+c,0<b<c+a,0<c<a+b} (Kimberling ...

The Johnson triangle DeltaJ_AJ_BJ_C, a term coined here for the first time, is the triangle formed by the centers of the Johnson circles. It has trilinear vertex matrix ...

A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing three equal squares such that each square ...

By analogy with the outer Napoleon triangle, consider the external erection of three squares on the sides of a triangle DeltaABC. These centers form a triangle DeltaO_AO_BO_C ...

The product of three translations along the directed sides of a triangle through twice the lengths of these sides is the identity map.

There are three theorems related to pedal circles that go under the collective title of the Fontené theorems. The first Fontené theorem lets DeltaABC be a triangle and P an ...

The trilinear quotient of two points p:q:r and u:v:w is the point p/u:q/v:r/w.

The circumcircle of an ellipse, i.e., the circle whose center concurs with that of the ellipse and whose radius is equal to the ellipse's semimajor axis.

The circumcircle of the Cevian triangle DeltaA^'B^'C^' of a given triangle DeltaABC with respect to a point P. The following table summarizes a number of named Cevian circles ...

Draw a triangle DeltaA_1A_2A_3, and let A_1^' be the intersection of the parallel to A_3A_1 through A_2 (the A_2-exmedian) and the parallel to A_1A_2 through A_3 (the ...