Fermat spiral

A planar transcendental curve the equation of which in polar coordinates has the form

$$\rho=a\sqrt\phi.$$

To each value of $\phi$ correspond two values of $\rho$ — a positive and a negative one. The Fermat spiral is centrally symmetric relative to the pole, which is a point of inflection. It belongs to the class of so-called algebraic spirals.

They were first studied by P. Fermat (1636).

Figure: f038420a

References

[1]	A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)

References

[a1]	J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)