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Difference between revisions of "Fermat spiral"

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They were first studied by P. Fermat (1636).
 
They were first studied by P. Fermat (1636).
  
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/f038420a.gif" />
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[[File:Fermat spiral.svg|center|400px|Fermat spiral]]
 
 
Figure: f038420a
 
  
 
====References====
 
====References====
<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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* {{Ref|1}} A.A. Savelov,  "Planar curves" , Moscow  (1960)  (In Russian)
 
 
 
 
 
 
====Comments====
 
 
 
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.D. Lawrence,  "A catalog of special plane curves" , Dover, reprint  (1972)</TD></TR></table>
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.D. Lawrence,  "A catalog of special plane curves" , Dover, reprint  (1972)</TD></TR></table>

Latest revision as of 19:35, 16 March 2023

A planar transcendental curve the equation of which in polar coordinates has the form

$$\rho=a\sqrt\phi.$$

To each value of $\phi$ correspond two values of $\rho$ — a positive and a negative one. The Fermat spiral is centrally symmetric relative to the pole, which is a point of inflection. It belongs to the class of so-called algebraic spirals.

They were first studied by P. Fermat (1636).

Fermat spiral

References

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

References

[a1] J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)
How to Cite This Entry:
Fermat spiral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fermat_spiral&oldid=52724
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article