An Archimedean spiral is a
spiral with polar
is the radial distance, is the polar angle, and is a constant which determines how tightly the spiral is "wrapped."
corresponding to particular special named spirals are summarized in the following
table, together with the colors with which they are depicted in the plot above.
curvature of an Archimedean spiral is given by
arc length for by
is a hypergeometric function.
If a fly crawls radially outward along a uniformly spinning disk, the curve it traces with respect to a reference frame in which the disk is at rest is an Archimedean spiral (Steinhaus 1999, p. 137). Furthermore, a heart-shaped frame composed of two arcs of an Archimedean spiral which is fixed to a rotating disk converts uniform rotational motion to uniform back-and-forth motion (Steinhaus 1999, pp. 136-137).
See also Archimedean Spiral Inverse Curve
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References Gray, A. Boca
Raton, FL: CRC Press, pp. 90-92, 1997. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Lauwerier, H. Princeton, NJ: Princeton University
Press, pp. 59-60, 1991. Fractals:
Endlessly Repeated Geometric Figures. Lawrence, J. D. New York: Dover, pp. 186 and 189, 1972. A
Catalog of Special Plane Curves. Lockwood,
E. H. Cambridge, England: Cambridge University Press, p. 175,
Book of Curves. MacTutor History of Mathematics Archive. "Spiral of Archimedes."
T. "The Spiral of Archimedes." San Carlos, CA: Wide World Publ./Tetra, p. 149,
Joy of Mathematics. Steinhaus, H. New York: Dover, pp. 136-137, 1999. Mathematical
Snapshots, 3rd ed. Wells,
pp. 8-9, 1991. The
Penguin Dictionary of Curious and Interesting Geometry. Cite this as:
Weisstein, Eric W. "Archimedean Spiral."
From --A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/ArchimedeanSpiral.html