Namespaces
Variants
Actions

Difference between revisions of "Lituus"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(TeX)
Line 1: Line 1:
 +
{{TEX|done}}
 
A plane transcendental curve whose equation in polar coordinates is
 
A plane transcendental curve whose equation in polar coordinates is
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l059/l059750/l0597501.png" /></td> </tr></table>
+
$$\rho=\frac{a}{\sqrt\phi}.$$
  
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/l059750a.gif" />
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/l059750a.gif" />
Line 7: Line 8:
 
Figure: l059750a
 
Figure: l059750a
  
To every value of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l059/l059750/l0597502.png" /> correspond two values of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l059/l059750/l0597503.png" />, one positive and one negative. The curve consists of two branches, that both approach the pole asymptotically (see Fig.). The line <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l059/l059750/l0597504.png" /> is an asymptote at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l059/l059750/l0597505.png" />, and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l059/l059750/l0597506.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l059/l059750/l0597507.png" /> are points of inflection. The lituus is related to the so-called algebraic [[Spirals|spirals]].
+
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|spirals]].
  
 
====References====
 
====References====

Revision as of 11:09, 26 July 2014

A plane transcendental curve whose equation in polar coordinates is

$$\rho=\frac{a}{\sqrt\phi}.$$

Figure: l059750a

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)


Comments

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=32535
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article