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
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.23$: Evolutes and Involutes. The Evolute of a Cycloid
