Definition:Involute

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