TOPICS
Search

Spiral

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
Spirals

A spiral is a curve that gets farther away from a central point as the angle is increased, thus "wrapping around" itself. The simplest example is Archimedes' spiral, whose radial distance increases linearly with angle. A number of named cases are illustrated above and summarized in the following table.

spiralradial formula
Archimedean spiralr=atheta^(1/n)
Archmedes' spiralr=atheta
atom spiralr=theta/(theta-a)
circle involute
Cornu spiral
Cotes' spiral
epispiralr=asec(ntheta)
Fermat's spiralr=atheta^(1/2)
Galilean spiralr=btheta^2-a
hyperbolic spiralr=a/theta
lituusr=atheta^(-1/2)
logarithmic spiralr=ae^(btheta)
Nielsen's spiral
polygonal spiral
Theodorus spiral
tractrix spiral

See also

Archimedes' Spiral, Circle Involute, Conical Spiral, Cornu Spiral, Cotes' Spiral, Daisy, Epispiral, Fermat's Spiral, Helix, Hyperbolic Spiral, Logarithmic Spiral, Mice Problem, Nielsen's Spiral, Phyllotaxis, Poinsot's Spirals, Polygonal Spiral, Rational Spiral, Spherical Spiral, Theodorus Spiral

Explore with Wolfram|Alpha

References

Davis, P. J. Spirals from Theodorus to Chaos. Wellesley, MA: A K Peters, 1993.Eppstein, D. "Spirals." http://www.ics.uci.edu/~eppstein/junkyard/spiral.html.Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 54-66, 1991.Lockwood, E. H. "Spirals." Ch. 22 in A Book of Curves. Cambridge, England: Cambridge University Press, pp. 172-175, 1967.Weisstein, E. W. "Books about Spirals." http://www.ericweisstein.com/encyclopedias/books/Spirals.html.Yates, R. C. "Spirals." A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 206-216, 1952.

Cite this as:

Weisstein, Eric W. "Spiral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Spiral.html

Subject classifications