Fermat's Spiral

Polar equation:
r2=a2θr^{2} = a^{2} \theta


This spiral was discussed by Fermat in 1636.

For any given positive value of θ there are two corresponding values of rr, one being the negative of the other. The resulting spiral will therefore be symmetrical about the liney=xy = -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 r2=a2/θr^{2} = a^{2}/ \theta.

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.