The lituus is an Archimedean spiral with n=-2, having polar equation


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.

The arc length, curvature, and tangential angle are given by


where the arc length is measured from theta=theta_0.

See also

Archimedean Spiral

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Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 221, 1987.Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 91, 1997.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.", D. E. History of Mathematics, Vol. 2: Special Topics of Elementary Mathematics. New York: Dover, p. 329, 1958.

Cite this as:

Weisstein, Eric W. "Lituus." From MathWorld--A Wolfram Web Resource.

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