Definition:Cissoid of Diocles
Definition
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 merely as 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.
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 11$: Special Plane Curves: Cissoid of Diocles: $11.34$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1 \cdotp 25992 \, 10498 \, 94873 \, 16476 \ldots$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): cissoid
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 25992 \, 10498 \, 94873 \, 16476 \ldots$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cissoid
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cissoid
- Weisstein, Eric W. "Cissoid of Diocles." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CissoidofDiocles.html