Hippopede of Eudoxus

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Eudoxus of Cnidus was a philosopher, astronomer, mathematician, physician, and a pupil of Plato. None of his work has come down to us; all of the references that we have come from secondary sources. He was born in Cnidus, currently in Turkey, about 400 BC.


One of his inventions was the hippopede, which is Greek for "horse fetter". This curve can be interpreted as the intersection of a cylinder and a sphere that have a point of tangency in common.

The curve can also be interpreted as the result of rotating segments as in the Demonstration. Both red segments maintain the same angle with the blue segment, which is always perpendicular to the green segment.


Contributed by: Daniel Domínguez Vázquez and Carlos Fajardo Sánchez (April 2012)
With additional contributions by: Pablo Alberca Bjerregaard
Open content licensed under CC BY-NC-SA



Based partially on "La hipopede de Eudoxo".

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