Parabolic spiral
From HandWiki
A transcendental plane curve whose equation in polar coordinates has the form \begin{equation} \rho = a\sqrt{\phi} + l,\quad l>0. \end{equation} To each value of $\phi$ correspond two values of $\sqrt{\phi}$, one positive and one negative.
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/p071250a.gif" />
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) |
| [a1] | F. Gomez Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971) |
| [a2] | J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972) |
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