Lituus (mathematics)

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This article is about spiral. For Roman wand, see Lituus.
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.

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