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BERNOULLIAN QUARTIC

Curve studied by Jakob Bernoulli in 1687 and Leibniz in 1696.
Jakob Bernoulli (1654 - 1705): Swiss mathematician.

 
Cartesian equation:  (a ³ b), or .
Quartic of genus 1.
Total area:  (equal to that of the smaller circle).

The Bernoullian quartic is the polyzomal curve median of two concentric circles.

It can be obtained mechanically by a slider-crank mechanism:

It's also the glissette of the centre of an ellipse bound to stay tangent, at a fixed point, to a fixed line:
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© Robert FERRÉOL  2017