Definition:Cissoid of Diocles

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The cissoid of Diocles is the plane curve defined in Cartesian coordinates as:

$x \paren {x^2 + y^2} = 2 a y^2$

or in polar coordinates as:

$r = 2 a \sin \theta \tan \theta$

for some real constant $a \in \R_{> 0}$.


The above diagram illustrates the cissoid of Diocles.

Also known as

Some sources refer to the cissoid of Diocles as merely a cissoid, but that term is best used to refer to the more general object of which the cissoid of Diocles was the original instance.

Source of Name

This entry was named for Diocles of Carystus.

Historical Note

Diocles of Carystus designed the curve now known as the cissoid of Diocles specifically for solving the problem of Doubling the Cube.

It can also be used to divide an angle into any proportion.