Lituus (mathematics)

In mathematics, a lituus is a spiral with polar equation

${\displaystyle r^{2}\theta =k}$

Branch for positive r

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

${\displaystyle (\theta ,r)=\left({\tfrac {1}{2}},\pm {\sqrt {2k}}\right).}$

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.

External links

• "Lituus", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
• Weisstein, Eric W. "Lituus". MathWorld.
• Interactive example using JSXGraph
• O'Connor, John J.; Robertson, Edmund F., "Lituus", MacTutor History of Mathematics archive, University of St Andrews.
• https://hsm.stackexchange.com/a/3181 on the history of the lituus curve.