Lituus (mathematics)

In mathematics, a lituus is a spiral in which the angle is inversely proportional to the square of the radius (as expressed in polar coordinates).

\( r^2\theta = k \, \)

This spiral, which has two branches depending on the sign of r, is asymptotic to the x axis. Its points of inflexion are at \( (\theta, r) = (\tfrac12, \sqrt{2k}) and (\tfrac12 , -\sqrt{2k}). \)

The curve was named by Roger Cotes in a collection of papers entitled Harmonia Mensurarum (1722), which was published six years after his death.

External links

Weisstein, Eric W., "Lituus" from MathWorld.
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