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 (θ, r) = (½, $\sqrt 2 k$ ) and (-½, - $\sqrt 2 k$ ).

The curve was named by Roger Cotes in a collection of papers entitled Harmonia Mensurarum (1722), which was published six years after his death.