Lituus spiral

Branch for positive r

In mathematics, a lituus spiral is a spiral in which (expressed in polar coordinates) the angle is inversely proportional to the square of the radius . The following applies in formulas ${\displaystyle \theta }$ ${\displaystyle r}$

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

This spiral, the two branches of which depend on the sign of , is asymptotic to the -axis. Your turning points are at and . ${\displaystyle r}$ ${\displaystyle x}$ ${\displaystyle (\theta ,r)=({\tfrac {1}{2}},{\sqrt {2k}})}$ ${\displaystyle ({\tfrac {1}{2}},-{\sqrt {2k}})}$

The curve was named after the Roman lituus , first by Roger Cotes in a collection of publications entitled Harmonia Mensurarum (1722) published six years after his death.

If you mirror a lituus spiral on the unit circle, you get a Fermat's spiral .

Web links

Commons : Lituus  - album with pictures, videos and audio files

• Eric W. Weisstein : Lituus . In: MathWorld (English).
• John J. O'Connor, Edmund F. Robertson :  Lituus. In: MacTutor History of Mathematics archive .
• Interactive example with JSXGraph