## hippopedeThe hippopede is a quartic curve described by the equation x^{2} + y^{2})^{2} + 4b(b - a)(x^{2} + y^{2}) - 4b^{2}x^{2} = 0
where a and b are positive constants. "Hippopede" means
literally "foot of a horse." It is often known as the hippopede
of Proclus, after Proclus who was
the first to study it, together with Eudoxus (who used it in his theory of how the planets move), and also the horse
fetter and the curve of Booth because of work
done on it by J. Booth (1810–1878). Any hippopede is the intersection of a torus (donut) with one of its tangent planes – that is, a plane parallel to its axis of rotational symmetry. The curve takes any of a variety of forms depending on where the donut is sliced. It may be a simple oval, an indented oval or elliptical lemniscate of Booth (0 < b < a),
two isolated circles, or a figure-eight curve
or hyperbolic lemniscate of Booth (0 < a < b). ## Related category• PLANE CURVES | |||||

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