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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))*