Perseus (Greek:Περσεύς; c. 150 BC) was anancient Greekgeometer, who invented the concept ofspiric sections, in analogy to theconic sections studied byApollonius of Perga.
Few details of Perseus' life are known, as he is mentioned only byProclus andGeminus; none of his own works have survived.
The spiric sections result from the intersection of atorus with aplane that is parallel to the rotational symmetry axis of the torus. Consequently, spiric sections are fourth-order (quartic)plane curves, whereas theconic sections are second-order (quadratic)plane curves. Spiric sections are a special case of atoric section, and were the first toric sections to be described.
The most famous spiric section is theCassini oval, which is thelocus of points having a constantproduct 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.
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