Editing Pythagoras (section)

== Attributed discoveries ==
=== 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}}

=== In music ===
[[File:Gaffurio Pythagoras.png|thumb|alt=Woodcut showing four scenes. In the upper right scene, blacksmiths are pounding with hammers. In the upper left scene, a man labelled "Pitagora" is shown playing different-sized bells and glasses with different amounts of liquid in them. Both the bells and glasses are labelled. In the bottom left scene, "Pitagora" is striking chords of different length laid out across a table, once again, all of which have numbers labels. In the bottom right scene, "Pitagora" and another man labeled "Phylolavs" are shown playing auloi.|Late medieval woodcut from [[Franchinus Gaffurius|Franchino Gafurio]]'s ''Theoria musice'' (1492), showing Pythagoras with bells and other instruments in Pythagorean tuning{{sfnp|Gregory|2015|page=28}}]]
{{See also|Pythagorean tuning |Pythagorean hammers}}
According to legend, Pythagoras discovered that musical notes could be translated into mathematical equations when he passed blacksmiths at work one day and heard the sound of their [[Pythagorean hammers|hammers]] clanging against the anvils.{{sfnp|Riedweg|2005|pages=27–28}}{{sfnp|Gregory|2015|page=27}} Thinking that the sounds of the hammers were beautiful and harmonious, except for one,{{sfnp|Riedweg|2005|page=28}} he rushed into the [[blacksmith]] shop and began testing the hammers.{{sfnp|Riedweg|2005|page=28}} He then realized that the tune played when the hammer struck was directly proportional to the size of the hammer and therefore concluded that music was mathematical.{{sfnp|Gregory|2015|page=27}}{{sfnp|Riedweg|2005|page=28}}

=== In astronomy ===
In ancient times, Pythagoras and his contemporary [[Parmenides|Parmenides of Elea]] were both credited with having been the first to teach that the [[Spherical Earth|Earth was spherical]],{{sfnp|Burkert|1972|page=306}} the first to divide the globe into [[Geographical zone|five climatic zones]],{{sfnp|Burkert|1972|page=306}} and the first to identify the [[Phosphorus (morning star)|morning star]] and the [[Hesperus|evening star]] as the same celestial object (now known as [[Venus]]).{{sfnp|Burkert|1972|pages=307–308}} Of the two philosophers, Parmenides has a much stronger claim to having been the first{{sfnp|Burkert|1972|pages=306–308}} and the attribution of these discoveries to Pythagoras seems to have possibly originated from a [[pseudepigrapha]]l poem.{{sfnp|Burkert|1972|pages=307–308}} [[Empedocles]], who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical.{{sfnp|Kahn|2001|page=53}} By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals.{{sfnp|Dicks|1970|page=68}}