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 Nelson You 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