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Class of quartic plane curves
In geometry, a hippopede (from Ancient Greek ἱπποπέδη (hippopédē) 'horse fetter') is a plane curve determined by an equation of the form ( x 2 + y 2 )
Hippopede
Figure-eight-shaped curve
quartic plane curves: the hippopede or lemniscate of Booth, the lemniscate of Bernoulli, and the lemniscate of Gerono. The hippopede was studied by Proclus
Lemniscate
Greek astronomer and mathematician (c.390–c.340 BC)
could make a point on the inner sphere trace out a figure-eight shape, or hippopede. Callippus, a Greek astronomer of the 4th century, added seven spheres
Eudoxus_of_Cnidus
Bow curve Bullet-nose curve Cruciform curve Deltoid curve Devil's curve Hippopede Kampyle of Eudoxus Kappa curve Lemniscate of Booth Lemniscate of Gerono
Gallery_of_curves
Ancient Greek geocentric cosmological model
were supposed to move in a way that created a curve known as a hippopede. The hippopede was a way to try to explain the retrograde motions of planets.
Concentric_spheres
Plane algebraic curve defined by a 4th-degree polynomial
are included in the family of toric sections and include the family of hippopedes and the family of Cassini ovals. The name is from σπειρα meaning torus
Plane_quartic_curve
Conceptual tool in astronomy
as On Speeds (Ancient Greek: Περί Ταχών) and asserted the shape of the hippopede or lemniscate was associated with planetary retrogression. Aristotle emphasized
Celestial_sphere
Cartesian oval Conchoid of Dürer Cruciform curve Deltoid curve Devil's curve Hippopede Kampyle of Eudoxus Kappa curve Lemniscate Lemniscate of Booth Lemniscate
List_of_curves
Bow curve Bullet-nose curve Cruciform curve Deltoid curve Devil's curve Hippopede Kampyle of Eudoxus Kappa curve Lemniscate of Booth Lemniscate of Gerono
List_of_mathematical_shapes
Greek geometer Perseus in roughly 150 BC. Well-known examples include the hippopede and the Cassini oval and their relatives, such as the lemniscate of Bernoulli
Toric_section
Mathematical object
are included in the family of toric sections and include the family of hippopedes and the family of Cassini ovals. The name is from σπειρα meaning "torus"
Spiric_section
Curve generated by the projections of a fixed point on the tangents of another curve
{\displaystyle {a^{2}}\cos ^{2}\theta \pm {b^{2}}\sin ^{2}\theta =r^{2}} (a hippopede) Rectangular hyperbola Center Lemniscate of Bernoulli Logarithmic spiral
Pedal_curve
Austrian-American mathematician (1899–1990)
240–56. "The Study of Wretched Subjects." Isis 42 (1951): 111. "On the 'Hippopede' of Eudoxus." Scripta Mathematica 19 (1953): 225–29. "Apollonius' Planetary
Otto_E._Neugebauer
were supposed to move in a way that created a curve known as a hippopede. The hippopede was a way to try and explain the retrograde motions of planets
Historical models of the Solar System
Historical_models_of_the_Solar_System
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
Mendell, Henry (1998), "Reflections on Eudoxus, Callippus and their Curves: Hippopedes and Callippopedes", Centaurus, 40 (3–4): 177–275, doi:10.1111/J.1600-0498
Ancient_Greek_mathematics
model are represented as rings here, each turning with the same period but in opposite directions, moving the planet along a figure-eight, or hippopede
Discovery and exploration of the Solar System
Discovery_and_exploration_of_the_Solar_System
Curve created by a geometric operation
{\displaystyle \left(x^{2}+y^{2}\right)^{2}=cx^{2}+dy^{2}} which is the hippopede. When d = −c this is the lemniscate of Bernoulli. Applying the degree
Inverse_curve
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