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A spiral discovered by Fermat in 1636. It is defined by the polar equation r^{2} = a^{2}θ.

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.

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