# 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 $C$.

This article is complete as far as it goes, but it could do with expansion.In particular: Tangent definition, as per NelsonYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Expand}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Also see

- 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 - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**involute** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**involute**