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 for the ancient Roman lituus by Roger Cotes in a collection of papers entitled Harmonia Mensurarum (1722), which was published six years after his death.

External links

• Hazewinkel, Michiel, ed. (2001), "Lituus", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
• Weisstein, Eric W., "Lituus", MathWorld.
• Interactive example using JSXGraph
• O'Connor, John J.; Robertson, Edmund F., "Lituus", MacTutor History of Mathematics archive, University of St Andrews.