Lituus

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Lituus (mathematics)

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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

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Wikipedia on Answers.com This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article Lituus (mathematics). Read