Editing Pythagoras (section)

=== In mathematics ===
[[File:Pythagorean.svg|thumb|upright=1.1|alt=Diagram illustrating the Pythagorean theorem|'''[[Pythagorean theorem|The Pythagorean theorem]]''': The sum of the areas of the two squares on the legs (''a'' and ''b'') equals the area of the square on the hypotenuse (''c'').]]

Although Pythagoras is most famous today for his alleged mathematical discoveries,{{sfnp|Kahn|2001|pages=1–2}}{{sfnp|Gregory|2015|pages=21–22}} classical historians dispute whether he himself ever actually made any significant contributions to the field.{{sfnp|Burkert|1972|pages=428–433}}{{sfnp|Kahn|2001|pages=2–3}} Many mathematical and scientific discoveries were attributed to Pythagoras, including [[Pythagorean theorem|his famous theorem]],<ref>{{harvp|Diog VIII|loc=§1.12}}; {{harvnb|Plutarch, Non posse suav. vivi sec. Ep.|loc=§1094|pp=67–71}}</ref> as well as discoveries in the fields of [[Music of ancient Greece|music]],<ref>Porphyry, in ''Ptol. Harm.'' p. 213; {{harvp|Diog VIII|loc=§1.12}}</ref> [[Greek astronomy|astronomy]],<ref>{{harvp|Diog VIII|loc=§1.14}}; Pliny, ''Hist. Nat.'' ii. 8.</ref> and [[Ancient Greek medicine|medicine]].<ref>{{harvp|Diog VIII|loc=§1.12}}, 14, 32.</ref> Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem,{{sfnp|Kahn|2001|pages=32–33}}{{sfnp|Riedweg|2005|pages=26–27}} a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides"{{sfnp|Riedweg|2005|page=27}}—that is, <math>a^2 + b^2 = c^2</math>. According to a popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole ''[[hecatomb]]'', to the gods.{{sfnp|Riedweg|2005|page=27}}{{sfnp|Burkert|1972|page=428}} Cicero rejected this story as spurious{{sfnp|Riedweg|2005|page=27}} because of the much more widely held belief that Pythagoras forbade blood sacrifices.{{sfnp|Riedweg|2005|page=27}} Porphyry attempted to explain the story by asserting that the ox was actually made of [[dough]].{{sfnp|Riedweg|2005|page=27}}

The Pythagorean theorem was known and used by the [[Babylonian mathematics|Babylonians]] and [[Indian mathematics|Indians]] centuries before Pythagoras,{{sfnp|Burkert|1972|pages=429, 462}}{{sfnp|Riedweg|2005|page=27}}{{sfnp|Kahn|2001|page=32}} and Burkert rejects the suggestion that Pythagoras had anything to do with it,{{sfnp|Burkert|1972|page=429}} noting that Pythagoras was never credited with having proved any theorem in antiquity.{{sfnp|Burkert|1972|page=429}} Furthermore, the manner in which the Babylonians employed Pythagorean numbers implies that they knew that the principle was generally applicable, and knew some kind of proof, which has not yet been found in the (still largely unpublished) [[cuneiform]] sources.{{efn|name=babylon}}