---
tag: E1PC4TZK5C
kind: concept
name: Involute
msc: [53A04]
sources:
  - url: https://en.wikipedia.org/wiki/Involute
same_as:
  wikidata: Q680712
  wikipedia: Involute
---

## Summary

An involute of a curve is the path traced by the end of a taut string that is unwound from the curve.
At each point it meets the tangent line of the original curve at a right angle.
Involutes and [[evolutes|Y3ZNV24V2C]] are inverse operations: the evolute of an involute is the original curve.
The involute of a circle is the profile of the teeth of most gears.

## Explanations

### L1 human

Wrap a string tightly around a spool and hold its free end.
Pull the string away so it stays tight, and unwind it.
The free end draws a spiral-like curve: this is the involute of the circle.
Different starting lengths of string give different involutes, all parallel to each other.