Parabolic spiral
From Encyclopedia of Mathematics
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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.
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) |
Comments
References
[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) |
How to Cite This Entry:
Parabolic spiral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Parabolic_spiral&oldid=28966
Parabolic spiral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Parabolic_spiral&oldid=28966
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article