**Polar equation: **

*r*^{2} = *a*^{2}*θ*

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

If your browser can handle JAVA code, click HERE 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.

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JOC/EFR/BS January 1997

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