Lituus
From Encyclopedia of Mathematics
A plane transcendental curve whose equation in polar coordinates is
$$\rho=\frac{a}{\sqrt\phi}.$$
To every value of $\phi$ correspond two values of $\rho$, one positive and one negative. The curve consists of two branches, that both approach the pole asymptotically (see Fig.). The line $\phi=0,\phi=\pi$ is an asymptote at $\rho=\pm\infty$, and $(1/2,a\sqrt2)$ and $(-1/2,-a\sqrt2)$ are points of inflection. The lituus is related to the so-called algebraic spirals.
References
- [1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)
References
[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: http://encyclopediaofmath.org/index.php?title=Lituus&oldid=52722
Lituus. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lituus&oldid=52722
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article