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The equilateral cevian triangle point of a triangle is the unique point P such that the Cevian triangle of P is equilateral. This point is Kimberling center X_(370).

"The" Griffiths point Gr is the fixed point in Griffiths' theorem. Given four points on a circle and a line through the center of the circle, the four corresponding Griffiths ...

The Jerabek center is the center of the Jerabek hyperbola. It is Kimberling center X_(125), which has equivalent triangle center functions alpha_(125) = cosAsin^2(B-C) (1) ...

The Kiepert center is the center of the Kiepert hyperbola. It is Kimberling center X_(115), which has equivalent triangle center functions alpha_(115) = ((b^2-c^2)^2)/a (1) ...

A triangle center alpha:beta:gamma is called a major triangle center if the triangle center function alpha=f(a,b,c,A,B,C) is a function of angle A alone, and therefore beta ...

A triangle tiling is a tiling of the plane by identical triangles. Any triangle tiles the plane (Wells 1991, p. 208). The total number of triangles (including inverted ones) ...

Consider two directly similar triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 with B_1C_1:A_1C_1:A_1B_1=B_2C_2:A_2C_2:A_2B_2=a:b:c. Then a·A_1A_2, b·B_1B_2 and c·C_1C_2 form the ...

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle ...

If P is a point on the circumcircle of a reference triangle, then the line PP^(-1), where P^(-1) is the isogonal conjugate of P, is called the antipedal line of P. It is a ...

Barycentric coordinates (t_1,t_2,t_3) normalized so that they become the areas of the triangles PA_1A_2, PA_1A_3, and PA_2A_3, where P is the point whose coordinates have ...