Lituus (mathematics)

This article is about spiral. For Roman wand, see Lituus.

Branch for positive r

In mathematics, a lituus is a spiral with polar equation

$r^{2}\theta =k$

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 $(\theta ,r)=({\tfrac {1}{2}},{\sqrt {2k}})$ and $({\tfrac {1}{2}},-{\sqrt {2k}})$.

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.