The conic ABCPP• and the affine mapping TP

Conic CP passing through the five points ABCPQ, where ABC is a given ordinary triangle and Q=cP• is the isotomcomplement of P, defined as the complement of the isotomic conjugate P• of P with respect to triangle ABC.

The map TP is the affine map which takes triangle ABC to the cevian triangle DEF of P with respect to ABC.
The map TP• is the affine map which takes triangle ABC to the cevian triangle D'E'F' of P• with respect to ABC.

cP• is a fixed point of TP, cP is a fixed point of TP• and Z (center of the conic CP) is a fixed point of TP• º TP-1.

The conic CP is parabola if and only if P lies on the Tucker nodal cubic (K015).

The conic CP is rectangular hyperbola if and only if P lies on the Lucas cubic (K007).



http://amontes.webs.ull.es/otrashtm/HGT2016.htm
Angel Montesdeoca. Octubre, 2016