Definition:Cissoid of Diocles

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Let $C$ be a circle of radius $a$ with a distinguished point $O$ on its circumference.

Let $L$ be the tangent to $C$ at the other end of the diameter of $C$ through $O$.

Let $R$ be a point on the circumference of $C$.

Let $OR$ be produced to meet $L$ at $S$.

Let $P$ be the point on $OS$ such that $OP$ = $RS$.

The cissoid of Diocles is the locus of points $P$ as $R$ travels around the circumference of $C$.


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.

Also see

  • Results about the cissoid of Diocles can be found here.

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 in about $180$ BCE, specifically for solving the problem of Doubling the Cube.

It was given its name by Geminus of Rhodes about a century later.

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