# Definition:Involute

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## Definition

Consider a curve $C$ embedded in a plane.

Imagine an ideal (zero thickness) cord $K$ wound round $C$.

The **involute** of $C$ is the locus of the end of $K$ as it is unwound from $C$.

## Also see

- Definition:Evolute
- Results about
**involutes**can be found here.

## Historical Note

The concept of the involute of a curve in the plane was first introduced by Christiaan Huygens during his analysis of the cycloid in his $1673$ treatise *Horologium Oscillatorium sive de Motu Pendularium*.

## Sources

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 11$: Special Plane Curves: Involute of a Circle: $11.28$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.23$: Evolutes and Involutes. The Evolute of a Cycloid