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.