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The points of intersection of the adjacent angle trisectors of the angles of any triangle DeltaABC are the polygon vertices of an equilateral triangle DeltaDEF known as the ...

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the P-anticomplementary conjugate of U is the point where h(a,b,c,p,q,r,u,v,w) ...

The vertex of an isosceles triangle having angle different from the two equal angles is called the apex of the isosceles triangle. The common polygon vertex at the top of 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 ...

The triangle center with triangle center function alpha=A.

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the cevapoint of P and U is the point (pv+qu)(pw+ru):(qw+rv)(qu+pv) :(ru+pw)(rv+qw).

Vandeghen's (1965) name for the transformation taking points to their isotomic conjugates.

If P=p:q:r and U=u:v:w are distinct trilinear points, neither lying on a sideline of the reference triangle DeltaABC, then the crosssum of P and U is the point ...

A curve which can be turned continuously inside an equilateral triangle. There are an infinite number of delta curves, but the simplest are the circle and lens-shaped ...

The Droussent cubic is the triangle cubic with trilinear equation sum_(cyclic)(b^4+c^4-a^4-b^2c^2)aalpha(b^2beta^2-c^2gamma^2)=0. It passes through Kimberling centers X_n for ...