View source for Fermat spiral

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

<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/f/f038/f038420/f0384201.png" /></td> </tr></table>

To each value of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f038/f038420/f0384202.png" /> correspond two values of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f038/f038420/f0384203.png" /> — 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|spirals]].

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

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/f038420a.gif" />

Figure: f038420a

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,   "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR></table>



====Comments====


====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>