Editing Ancient Greek mathematics (section)

==== Mathematics in the time of Plato ====
While Plato was not a mathematician, numerous early mathematicians were associated with [[Plato]] or with his [[Platonic Academy|Academy]]. Familiarity with mathematicians' work is also reflected in several Platonic dialogues were mathematics are mentioned, including the ''[[Meno]]'', the ''[[Theaetetus (dialogue)|Theaetetus]]'', the ''[[Republic]]'', and the ''[[Timaeus (dialogue)|Timaeus]]''.{{sfn|Fowler|1999}}

[[Archytas]], a Pythagorean philosopher from Tarentum, was a friend of Plato who made several contributions to mathematics, including solving the problem of [[doubling the cube]], now known to be impossible with only a compass and a straightedge, using an alternative method. He also systematized the [[Pythagorean means|study of means]], and possibly worked on optics and mechanics.<ref>{{Cite journal |last=Burnyeat |first=M. F. |date=2005 |title=Archytas and Optics |url=https://www.cambridge.org/core/journals/science-in-context/article/abs/archytas-and-optics/BDBF3868CEF7004C16547836D66A4F24 |journal=Science in Context |volume=18 |issue=1 |pages=35–53 |doi=10.1017/S0269889705000347 |doi-broken-date=16 December 2024}}</ref> Archytas has been credited with early material found in Books VII–IX of the ''Elements'', which deal with [[elementary number theory]].{{sfn|Netz|2014}}

[[Theaetetus (mathematician)|Theaetetus]] is one of the main characters in the Platonic [[Theaetetus (dialogue)|dialogue named after him]], where he works on a problem given to him by [[Theodorus of Cyrene]] to demonstrate that the square roots of several numbers from 3 to 17 are irrational, leading to the construction now known as the [[Spiral of Theodorus]]. Theaetetus is traditionally credited with much of the work contained in Book X of the ''Elements'', concerned with [[incommensurable magnitudes]], and Book XIII, which outlines the construction of the [[regular polyhedra]]. Although some of the regular polyhedra were certainly known previously, he is credited with their systematic study and the proof that only five of them exist.<ref>Elements Book XIII, Proposition 18</ref>{{sfn|Acerbi|2018|pp=277-278}}

Another mathematician who might have visited Plato's Academy is [[Eudoxus of Cnidus]], associated with the theory of proportion found in Book V of the ''Elements''. [[Archimedes]] credits Eudoxus with a proof that the volume of a cone is one-third the volume of a cylinder with the same base, which appears in two propositions in Book XII of the ''Elements''.{{sfn|Acerbi|2018|p=279}} He also developed an astronomical calendar, now lost, that remains partially preserved in [[Aratus]]' poem ''[[Phaenomena]].''{{sfn|Netz|2022}} Eudoxus seems to have founded a school of mathematics in [[Cyzicus]], where one of Eudoxus' students, [[Menaechmus]], went on to develop a theory of conic sections.{{sfn|Netz|2022}}