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CORNOID
Curve studied by Alberto Sanchez in 1895. 
Cartesian parametrization: .
Cartesian equation: Rational sextic. 

Given a horizontal line cutting the circle with centre O and radius a at P and P', the cornoid is the locus of the projection M of P on the parallel to (OP) passing through P'.
Java applet for this construction: webs.ono.com/rpe/cornoide.htm
The cornoid is also the orthoptic of the Maltese cross.
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© Robert FERRÉOL 2017