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The curve has infinitely many double points and one [[Point_of_inflection | point of inflection]] (see Fig.). If $l=0$, then the curve is called the [[Fermat spiral|Fermat spiral]]. The parabolic spiral is related to the so-called algebraic spirals (see [[Spirals|Spirals]]).
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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|Fermat spiral]]. The parabolic spiral is related to the so-called algebraic spirals (see [[Spirals]]).
  
 
====References====
 
====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,  "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR></table>
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<table>
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<TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,  "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  F. Gomez Teixeira,  "Traité des courbes" , '''1–3''' , Chelsea, reprint  (1971)</TD></TR>
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<TR><TD valign="top">[a2]</TD> <TD valign="top">  J.D. Lawrence,  "A catalog of special plane curves" , Dover, reprint  (1972)</TD></TR>
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</table>
  
 
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====Comments====
 
 
 
 
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  F. Gomez Teixeira,  "Traité des courbes" , '''1–3''' , Chelsea, reprint  (1971)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  J.D. Lawrence,  "A catalog of special plane curves" , Dover, reprint  (1972)</TD></TR></table>
 

Latest revision as of 05:44, 9 April 2023


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)
[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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How to Cite This Entry:
Parabolic spiral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Parabolic_spiral&oldid=53696
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article