# Parabolic spiral

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A transcendental plane curve whose equation in polar coordinates has the form $$\rho = a\sqrt{\phi} + l,\quad l>0.$$ To each value of $\phi$ correspond two values of $\sqrt{\phi}$, one positive and one negative.

Figure: p071250a

The curve has infinitely many double points and one point of inflection (see Fig.). If $l=0$, then the curve is called the Fermat spiral. The parabolic spiral is related to the so-called algebraic spirals (see Spirals).

#### References

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