Perseus (geometer)

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.

Life

Few details of Perseus' life are known, as he is mentioned only by Proclus and Geminus; none of his own works have survived.

Spiric sections

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.

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 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'antiquité", Bull. des sciences mathématique et astronomique, 8, 19-30.
Heath TL. (1931) A history of Greek mathematics, vols. I & II, Oxford.
O'Connor, John J.; Robertson, Edmund F., "Perseus", MacTutor History of Mathematics archive, University of St Andrews .

Ancient Greek mathematics

Mathematicians	Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus

Treatises	Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Elements (Euclid) On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) The Sand Reckoner

Problems	Problem of Apollonius Squaring the circle Doubling the cube Angle trisection

Centers	Cyrene Library of Alexandria Platonic Academy

Timeline of Ancient Greek mathematicians

This article is issued from Wikipedia - version of the 11/26/2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.