Lituus (mathematics)

In mathematics, a lituus is a spiral with polar equation

r 2 θ = 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 ( θ , r ) = ( 1 2 , 2 k ) and ( 1 2 , − 2 k ) .

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.