Hippopede

A hippopede (meaning "horse fetter" in ancient Greek) is plane curve obeying the equation in polar coordinates

[r = 1 - a \sin^ \theta]

[\left(x^+y^ \right)^ = y^ + (1-a) x^]

The hippopede is a spiric section in which the intersecting plane is tangent to the interior of the torus. It was investigated by Proclus, Eudoxus and, more recently, J. Booth (1810-1878). For [a=2], the hippopede corresponds to the lemniscate of Bernoulli.

References

Lawrence JD. (1972) Catalog of Special Plane Curves, Dover.

Booth J. A Treatise on Some New Geometrical Methods, Longmans, Green, Reader, and Dyer, London, Vol. I (1873) and Vol. II (1877).

External links

[MathWorld description]
[2Dcurves.com description]

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