An Archimedean spiral with polar
equation
(1)
The hyperbolic spiral, also called the inverse spiral (Whittaker 1944, p. 83), originated with Pierre Varignon in 1704 and was studied by Johann Bernoulli between 1710 and 1713, as well as by Cotes in 1722 (MacTutor Archive).
It is also a special case of a Cotes' spiral , i.e.,
the path followed by a particle in a central orbit with power law
(2)
when
The curvature and tangential
angle are given by
See also Archimedean Spiral ,
Spiral
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References Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Cotes, R. Harmonia Mensurarum. p. 31 and 98, 1722. Gray,
A. Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Lawrence, J. D. A
Catalog of Special Plane Curves. Lockwood,
E. H. A
Book of Curves. MacTutor History of Mathematics Archive. "Hyperbolic Spiral."
http://www-groups.dcs.st-and.ac.uk/~history/Curves/Hyperbolic.html . Newton,
I. Book I, §2, Prop. IX in Philosophiae
Naturalis Principia Mathematica. Whittaker, E. T.
A
Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction
to the Problem of Three Bodies. Referenced
on Wolfram|Alpha Hyperbolic Spiral
Cite this as:
Weisstein, Eric W. "Hyperbolic Spiral."
From MathWorld https://mathworld.wolfram.com/HyperbolicSpiral.html
Subject classifications
is a constant and 
is the specific angular momentum.
