Lituus (mathematics)

Branch for positive r

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.
• Interactive example using JSXGraph