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[[File:Cochleoid-1.png| right| frame| Figure 1. The cochleoid ([[Media:Cochleoid-1.pdf|pdf]]) ]]
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A plane transcendental curve whose equation in polar coordinates is
 
A plane transcendental curve whose equation in polar coordinates is
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\begin{equation}
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\rho = a\frac{\sin\varphi}{\varphi}.
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\end{equation}
  
<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/c/c022/c022820/c0228201.png" /></td> </tr></table>
 
  
The cochleoid has infinitely many spirals, passing through its pole and touching the polar axis (see Fig.). The pole is a singular point of infinite multiplicity. Any straight line through the pole <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022820/c0228202.png" /> intersects the cochleoid; the tangents to the cochleoid at these intersection points pass through the same point.
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The cochleoid has infinitely many spirals, passing through its pole and touching the polar axis (see Fig.). The pole is a singular point of infinite multiplicity. Any straight line through the pole $O$ intersects the cochleoid; the tangents to the cochleoid at these intersection points pass through the same point.
  
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/c022820a.gif" />
 
  
Figure: c022820a
 
  
 
====References====
 
====References====

Revision as of 14:57, 14 February 2013


Figure 1. The cochleoid (pdf)

A plane transcendental curve whose equation in polar coordinates is \begin{equation} \rho = a\frac{\sin\varphi}{\varphi}. \end{equation}


The cochleoid has infinitely many spirals, passing through its pole and touching the polar axis (see Fig.). The pole is a singular point of infinite multiplicity. Any straight line through the pole $O$ intersects the cochleoid; the tangents to the cochleoid at these intersection points pass through the same point.


References

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


Comments

References

[a1] J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)
How to Cite This Entry:
Cochleoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cochleoid&oldid=29430
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article