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Difference between revisions of "Cochleoid"

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(Comment: inversion yields quadratrix of Hippias, ref Lawrence)
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====References====
 
====References====
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,  "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR></table>
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,  "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR></table>
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====Comments====
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The [[Inversion|inverse]] of the cochleoid with respect to the origin is the [[quadratrix of Hippias]].
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====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.D. Lawrence,  "A catalog of special plane curves" , Dover  (1972) ISBN 0-486-60288-5  {{ZBL|0257.50002}}</TD></TR></table>
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.D. Lawrence,  "A catalog of special plane curves" , Dover  (1972) ISBN 0-486-60288-5  {{ZBL|0257.50002}}</TD></TR></table>

Revision as of 21:06, 12 December 2017


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

The inverse of the cochleoid with respect to the origin is the quadratrix of Hippias.

References

[a1] J.D. Lawrence, "A catalog of special plane curves" , Dover (1972) ISBN 0-486-60288-5 Zbl 0257.50002
How to Cite This Entry:
Cochleoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cochleoid&oldid=42481
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article