A transcendental plane curve whose equation in polar coordinates has the form
To each value of correspond two values of , one positive and one negative.
The curve has infinitely many double points and one point of inflection (see Fig.). If , then the curve is called the Fermat spiral. The parabolic spiral is related to the so-called algebraic spirals (see Spirals).
|||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)|
Parabolic spiral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Parabolic_spiral&oldid=19135