Lituus

An Archimedean Spiral with $m=-2$, having polar equation

$$r^2\theta=a^2.$$

Lituus means a ``crook,'' in the sense of a bishop's crosier. The lituus curve originated with Cotes in 1722. Maclaurin used the term lituus in his book Harmonia Mensurarum in 1722 (MacTutor Archive). The lituus is the locus of the point $P$ moving such that the Area of a circular Sector remains constant.

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 69-70, 1993.

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 186 and 188, 1972.

Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, p. 175, 1967.

MacTutor History of Mathematics Archive. ``Lituus.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Lituus.html.