- Perseus (geometer)
Perseus (c.
150 BC ) was an ancient Greek geometer, who invented the concept ofspiric section s, in analogy to theconic section s studied byApollonius of Perga .Few details of Perseus' life are known, as he is mentioned only by
Proclus andGeminus ; none of his own works have survived.The spiric sections result from the intersection of a
torus with a plane that is parallel to the rotational symmetry axis of the torus. Consequently, spiric sections are fourth-order (quartic )plane curve s, whereas theconic section s are second-order (quadratic )plane curve s. Spiric sections are a special case of atoric section , and were the first toric sections to be described.The most famous spiric section is the
Cassini oval , which is the locus of points having a constant "product" of distances to two foci. For comparison, anellipse has a constant "sum" of focal distances, ahyperbola has a constant difference of focal distances and acircle has a constant ratio of focal distances.References
* Tannery P. (1884) "Pour l'histoire des lignes et de surfaces courbes dans l'antiquité", "Bull. des sciences mathématique et astronomique", 8, 19-30.
* Heath TL. (1931) "A history of Greek mathematics", vols. I & II, Oxford.
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