Curves

Fermat's Spiral

Description

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 $r^{2} = a^{2}/ \theta$.

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.

Associated Curves

Definitions of the Associated curves

Evolute

Involute 1

Involute 2

Inverse curve wrt origin

Inverse wrt another circle

Pedal curve wrt origin

Pedal wrt another point

Negative pedal curve wrt origin

Negative pedal wrt another point

Caustic wrt horizontal rays

Caustic curve wrt another point