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Fermat’s spiral

Fermat's spiral.

The parametric equations of the Fermat’s spiral can be given by

x=at12cos⁡t,y=at12sin⁡tx = at^{\frac{1}{2}} \cos t, \, y= at^{\frac{1}{2}} \sin t
x=−at12cos⁡t,y=−at12sin⁡tx = -at^{\frac{1}{2}} \cos t, \, y= -at^{\frac{1}{2}} \sin t

In polar coordinates the equation of a Fermat’s spiral with parameter aa and center/centre (0,0)\left(0,\,0\right) is given by

r2=a2θr^2=a^2 \theta

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