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A plane transcendental curve whose equation in polar coordinates is

Figure: l059750a

To every value of correspond two values of , one positive and one negative. The curve consists of two branches, that both approach the pole asymptotically (see Fig.). The line is an asymptote at , and and are points of inflection. The lituus is related to the so-called algebraic spirals.


[1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)



[a1] K. Fladt, "Analytische Geometrie spezieller ebener Kurven" , Akad. Verlagsgesell. (1962)
[a2] F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)
How to Cite This Entry:
Lituus. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article