Perseus (; c. 150 BC) was an

ancient Greek Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek ...

geometer, who invented the concept of spiric sections, in analogy to the

conic section A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, tho ...

s studied by

Apollonius of Perga Apollonius of Perga ( ; ) was an ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the earlier contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention o ...

Life

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

Proclus Proclus Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor (, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophers of late antiquity. He set forth one of th ...

and

Geminus Geminus of Rhodes (), was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the ''Introduction to the Phenomena'', still survives; it was intended as an introductory astronomy book for students ...

; none of his own works have survived.

Spiric sections

The spiric sections result from the intersection of a

torus In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanarity, coplanar with the circle. The main types of toruses inclu ...

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

s 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.

Examples

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 In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

has a constant sum of focal distances, a hyperbola has a constant difference of focal distances, and a

circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...

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. * {{DEFAULTSORT:Perseus Ancient Greek geometers 2nd-century BC Greek mathematicians