
This quartic curve has been studied by Eudoxus of Cnide (406-355 BC), an
astronomer, philosopher and mathematician who was a pupil of Plato.
Eudoxus
worked on the curve in relation to the classical problem of the duplication of the cube.
Let there be a circle C through O with radius √1/2, which cuts the kampyle in P.
Then OP has as length 3√2
In polar coordinates the curve can be written as r = cos -2 φ.
The kampyle 1) is also named Clairaut's curve.
And the kampyle is:
Its Cartesian equation resembles the equation of the lemniscate
of Gerono.
notes
1) Kampyle (Gr.) = curved
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