```
..............
...              ....
..                      ..
..                           ..
..          ...........          .
..        ..            ..         :
:        .                  :        :
..       :                    :       :
:       :        ......        :      ..
:       :       :      :       :       :
:      :.      :     .         :       :
:      ::      ..             :       :
:       :       ..          ..       ..
:        .        ....  ....        ..
:        .                        ..
:        .                      .
:         ..               ...         :
..          ..............          ..               .                                .
..                          ..
....                  ....
..................
```

The involute of a circle is the path traced out by a point on a straight line that rolls around a circle.

The involute of a circle was studied by Huygens when he was considering clocks without pendulums that might be used on ships at sea. He used the involute of a circle in his first pendulum clock in an attempt to force the pendulum to swing in the path of a cycloid.

The pedal of the involute of a circle, with the centre as pedal point, is a Spiral of Archimedes.

Of course the evolute of an involute of a circle is a circle.

Parametric Cartesian equation:
x = a(cos(t) + t sin(t)), y = a(sin(t) - t cos(t))

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