Lituus (mathematics)

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Branch for positive r

In mathematics, a lituus is a spiral with polar equation

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 , is asymptotic to the axis. Its points of inflexion are at and .

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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