**Polar equation: **

*r*^{2} = *a*^{2}*θ*

**Click below to see one of the Associated curves.**

Click THIS LINK to experiment interactively with this curve and its associated curves.

This spiral was discussed by Fermat in 1636.

For any given positive value of *θ* there are two corresponding values of *r*, one being the negative of the other. The resulting spiral will therefore be symmetrical about the line *y* = -*x* as can be seen from the curve displayed above.

The inverse of Fermat's Spiral, when the pole is taken as the centre of inversion, is the spiral *r*^{2} = *a*^{2}/*θ*.

For technical reasons with the plotting routines, when evolutes, involutes, inverses and pedals are drawn only one of the two branches of the spiral are drawn.

Main index | Famous curves index |

Previous curve | Next curve |

JOC/EFR/BS January 1997

The URL of this page is:

http://www-history.mcs.st-andrews.ac.uk/Curves/Fermats.html