**Perseus** (c.

150 BC) was an

ancient Greek geometer, who invented the concept of

spiric sections, in analogy to the

conic sections studied by

Apollonius of Perga.

Few details of Perseus' life are known, as he is mentioned only by

Proclus and

Geminus; 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 curves, whereas the

conic sections are second-order (

quadratic)

plane curves. Spiric sections are a special case of a

toric 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, an

ellipse has a constant

*sum* of focal distances, a

hyperbola has a constant difference of focal distances and a

circle has a constant ratio of focal distances.

## References

- Tannery P. (1884) "Pour l'histoire des lignes et de surfaces courbes dans l'antiquitÃ©",
*Bull. des sciences mathÃ©matique et astronomique*, **8**, 19-30.
- Heath TL. (1931)
*A history of Greek mathematics*, vols. I & II, Oxford.

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