PlanetMath: Archimedean spiral

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Archimedean spiral

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An Archimedean spiral is a spiral with the polar equation

$\displaystyle r=a\theta^{1/t},$

where

is a real,

is the radial distance, $\theta$ is the angle, and

is a constant.

The curvature of an Archimedean spiral is given by the formula

$\displaystyle \frac{t\theta^{1-1/t}(t^2 \theta^2 +t +1)}{a(t^2\theta^2 +1)^{3/2}}.$

$\includegraphics{as}$

"Archimedean spiral" is owned by rspuzio. [ full author list (2) | owner history (2) ]

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Cross-references: curvature, angle, distance, radial, real, equation, polar
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This is version 3 of Archimedean spiral, born on 2003-12-09, modified 2007-06-10.
Object id is 5486, canonical name is ArchimedeanSpiral.
Accessed 7343 times total.

Classification:

14H45 (Algebraic geometry :: Curves :: Special curves and curves of low genus)

Pending Errata and Addenda

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