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DOUBLE-HEART CURVE

Curve studied by Grégoire de Saint Vincent in 1647 and Cramer in 1750.
Homemade nickname: rabbit's ears.

 
Cartesian equation:  , i.e. .
Quartic of genus 1.

 
The double hearts are the polyzomal curves associated to two tangent circles, here the circles  and .
They are obtained by the slider-crank mechanism as follows:
Opposite, photograph of a real mechanism tracing this curve thanks to this method.
Another curve shaped like rabbit's ears, due to Sébastien Kerner: 
Not to be mistaken for the Viviani curve, including the regular bifolium. They are rational quartics.


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© Robert FERRÉOL, Jacques MANDONNET 2017