Lituus (mathematics)

Branch for positive r

In mathematics, a lituus is a spiral with polar equation

$r^{2}\theta =k$

where k is any non-zero constant. Thus, the angle $θ$ is inversely proportional to the square of the radius $r$ .

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) [1994], "Lituus", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, 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 .
https://hsm.stackexchange.com/a/3181 on the history of the lituus curve.

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