Definition:Involute
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Definition
Let $\CC$ be a curve $C$ embedded in a plane.
Definition $1$
Let $\LL$ be the locus of a fixed point on a tangent to $\CC$ as it rolls around $\CC$.
The curve $\LL$ is the involute of $\CC$.
Definition $2$
Imagine an ideal (zero thickness) cord $K$ wound round $\CC$.
The involute of $\CC$ is the locus of the end of $K$ as it is unwound from $\CC$.
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.