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{{Redirect|Pythagoras of Samos|the Samian statuary|Pythagoras (sculptor)}}
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{{Infobox philosopher
|region          = Western philosophy
|era              = [[Ancient philosophy]]
|image = Kapitolinischer Pythagoras adjusted.jpg
|caption = Bust of Pythagoras of Samos in the [[Capitoline Museums]], [[Rome]]
|name            = Pythagoras (Πυθαγόρας)
|birth_date      = c. 570 BC
|birth_place      = [[Samos]]
|death_date      = c. 495 BC (aged around 75)<!--PLEASE SEE TALK BEFORE CHANGING DATE-->
|death_place      = [[Metapontum]]
|school_tradition = [[Pythagoreanism]]
|main_interests  = [[Metaphysics]], [[Music]], [[Mathematics]], [[Ethics]], [[Politics]]
|influences      = [[Thales of Miletus|Thales]], [[Anaximander]], [[Pherecydes of Syros|Pherecydes]]
|influenced      = [[Philolaus]], [[Alcmaeon of Croton|Alcmaeon]], [[Parmenides]], [[Plato]], [[Euclid]], [[Empedocles]], [[Hippasus]], [[Johannes Kepler|Kepler]]
|notable_ideas    = [[Musica universalis]], [[Pythagorean tuning]], [[Pythagorean theorem]]
}}


'''Pythagoras of Samos''' ({{IPAc-en|p|ɪ|ˈ|θ|æ|g|ə|r|ə|s}}; {{lang-grc|Πυθαγόρας ὁ Σάμιος|Pythagóras ho Sámios|Pythagoras the [[Samos|Samian]]}}, or simply {{lang|grc|Πυθαγόρας}}; Πυθαγόρης in [[Ionian Greek]]; c. 570 BC – c. 495 BC)<ref>"The dates of his life cannot be fixed exactly, but assuming the approximate correctness of the statement of Aristoxenus (ap. Porph. ''V.P.'' 9) that he left Samos to escape the tyranny of Polycrates at the age of forty, we may put his birth round about 570 BC, or a few years earlier. The length of his life was variously estimated in antiquity, but it is agreed that he lived to a fairly ripe old age, and most probably he died at about seventy-five or eighty." [[William Keith Chambers Guthrie]], (1978), ''A history of Greek philosophy, Volume 1: The earlier Presocratics and the Pythagoreans'', page 173. Cambridge University Press</ref><ref>[http://www-groups.dcs.st-and.ac.uk/history/Biographies/Pythagoras.html Biographies]</ref> was an [[Ionians|Ionian]] [[Ancient Greeks|Greek]] [[Greek philosophy|philosopher]], [[mathematician]], and founder of the religious movement called [[Pythagoreanism]]. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of [[Samos]], and might have travelled widely in his youth, visiting [[Egypt]] and other places seeking knowledge. Around 530 BC, he moved to [[Crotone|Croton]], in [[Magna Graecia]], and there set up a religious sect. His followers pursued the religious rites and practices developed by Pythagoras, and studied his philosophical theories. The society took an active role in the politics of Croton, but this eventually led to their downfall. The Pythagorean meeting-places were burned, and Pythagoras was forced to flee the city. He is said to have died in [[Metapontum]].
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Pythagoras made influential contributions to [[philosophy]] and religious teaching in the late 6th century BC. He is often revered as a great [[mathematician]], [[mysticism|mystic]] and [[scientist]], but he is best known for the [[Pythagorean theorem]] which bears his name. However, because legend and obfuscation cloud his work even more than that of the other [[Pre-Socratic philosophy|pre-Socratic philosophers]], one can give only a tentative account of his teachings, and some have questioned whether he contributed much to [[mathematics]] and [[natural philosophy]]. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Whether or not his disciples believed that everything was related to mathematics and that numbers were the ultimate reality is unknown. It was said that he was the first man to call himself a philosopher, or lover of wisdom,<ref>[[Cicero]], ''[[Tusculan Disputations]]'', 5.3.8–9 = [[Heraclides Ponticus]] fr. 88 Wehrli, [[Diogenes Laërtius]] 1.12, 8.8, [[Iamblichus]] ''VP'' 58.  Burkert attempted to discredit this ancient tradition, but it has been defended by C.J. De Vogel, ''Pythagoras and Early Pythagoreanism'' (1966), pp. 97–102, and C. Riedweg, ''Pythagoras: His Life, Teaching, And Influence'' (2005), p. 92.</ref> and Pythagorean ideas exercised a marked influence on [[Plato]], and through him, all of [[Western philosophy]].
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Accurate facts about the life of Pythagoras are so few, and most information concerning him is of so late a date, and so untrustworthy, that it is impossible to provide more than a vague outline of his life. The lack of information by contemporary writers, together with the secrecy which surrounded the Pythagorean brotherhood, meant that invention took the place of facts. The stories which were created were eagerly sought by the [[Neoplatonist]] writers who provide most of the details about Pythagoras, but who were uncritical concerning anything which related to the [[Greek gods|gods]] or which was considered divine.<ref>Iamblichus, ''Adhort. ad Philos.'' p. 324, ed. Kiessling.</ref> Thus many myths were created – such as that [[Apollo]] was his father; that Pythagoras gleamed with a [[supernatural]] brightness; that he had a golden [[thigh]]; that [[Abaris the Hyperborean|Abaris]] came flying to him on a golden [[arrow]]; that he was seen in different places at the same time.<ref>Comp. Herodian, iv. 94, etc.</ref> With the exception of a few remarks by [[Xenophanes]], [[Heraclitus]], [[Herodotus]], [[Plato]], [[Aristotle]], and [[Isocrates]], we are mainly dependent on [[Diogenes Laërtius]], [[Porphyry (philosopher)|Porphyry]], and [[Iamblichus]] for the biographical details. Aristotle had written a separate work on the Pythagoreans, which unfortunately has not survived.<ref>He alludes to it himself, ''Met.'' i. 5. p. 986. 12, ed. Bekker.</ref> His disciples [[Dicaearchus]], [[Aristoxenus]], and [[Heraclides Ponticus]] had written on the same subject. These writers, late as they are, were among the best sources from whom Porphyry and Iamblichus drew, besides the legendary accounts and their own inventions. Hence historians are often reduced to considering the statements based on their inherent probability, but even then, if all the credible stories concerning Pythagoras were supposed true, his range of activity would be impossibly vast.<ref>{{SmithDGRBM}}</ref>
 
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==Life==
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[[File:Pythagoras Bust Vatican Museum.jpg|thumb|[[Bust (sculpture)|Bust]] of Pythagoras, [[Vatican Museums|Vatican]]]]
[[Herodotus]], [[Isocrates]], and other early writers all agree that Pythagoras was born on [[Samos]], the Greek island in the eastern [[Aegean Sea|Aegean]], and we also learn that Pythagoras was the son of Mnesarchus.<ref>Herodotus, iv. 95, Isocrates, ''Busiris'', 28–9; Later writers called him a Tyrrhenian or Phliasian, and gave Marmacus, or Demaratus, as the name of his father, Diogenes Laërtius, viii. 1; Porphyry, ''Vit. Pyth.'' 1, 2; Justin, xx. 4; Pausanias, ii. 13.</ref> His father was a gem-engraver or a merchant. His name led him to be associated with [[Pythia]]n [[Apollo]]; [[Aristippus]] explained his name by saying, "He spoke (''agor-'') the truth no less than did the Pythian (''Pyth-'')," and [[Iamblichus]] tells the story that the Pythia prophesied that his pregnant mother would give birth to a man supremely beautiful, wise, and beneficial to humankind.<ref>{{cite book|author= Riedweg, Christoph|title=Pythagoras: His Life, Teaching and Influence|publisher=[[Cornell University]]|year=2005|pages=5–6, 59, 73}}</ref> A late source gives his mother's name as Pythais.<ref>[[Apollonius of Tyana]] ap. Porphyry, ''Vit. Pyth.'' 2</ref> As to the date of his birth, [[Aristoxenus]] stated that Pythagoras left Samos in the reign of [[Polycrates]], at the age of 40, which would give a date of birth around 570 BC.<ref>Porphyry, ''Vit. Pyth.'' 9</ref>


It was natural for the ancient biographers to inquire as to the origins of Pythagoras' remarkable system. In the absence of reliable information, however, a huge range of teachers were assigned to Pythagoras. Some made his training almost entirely Greek, others exclusively [[Late Period of ancient Egypt|Egyptian]] and [[Oriental]]. We find mentioned as his instructors [[Creophylus of Samos|Creophylus]],<ref name="Iamblichus, Vit. Pyth. 9">Iamblichus, ''Vit. Pyth.'' 9</ref> [[Hermodamas of Samos]],<ref>Porphyry, ''Vit. Pyth.'' 2, Diogenes Laërtius, viii. 2 [http://books.google.co.uk/books?id=A8ixyQJA7_MC&pg=PA10&lpg=PA10&dq=teachers+of+Pythagoras+instructors&source=bl&ots=R1Nf9AFGWB&sig=JKF2yU5Gx0pW8ndITfrGlhHpTLU&hl=en&sa=X&ei=jmUyT5ryK4-dOpKE9d8G&sqi=2&ved=0CGUQ6AEwCA#v=onepage&q=teachers%20of%20Pythagoras%20instructors&f=false  C. Riedweg, S. Rendall]  ISBN 0-8014-7452-3 Retrieved 2012-02-08</ref> [[Bias of Priene|Bias]],<ref name="Iamblichus, Vit. Pyth. 9"/> [[Thales]],<ref name="Iamblichus, Vit. Pyth. 9"/> [[Anaximander]],<ref>Iamblichus, ''Vit. Pyth.'' 9; Porphyry, ''Vit. Pyth.'' 2</ref> and [[Pherecydes of Syros]].<ref>Aristoxenus and others in Diogenes Laërtius, i. 118, 119; Cicero, ''de Div.'' i. 49</ref> He is said too, to have been taught by a [[Pythia|Delphic]] priestess named [[Themistoclea]], who introduced him to the principles of [[ethics]].<ref>[http://books.google.com.br/books?id=x7ngECDpxmMC&printsec=frontcover Mary Ellen Waithe, ''Ancient women philosophers, 600 B.C.–500 A.D.'', p. 11]</ref><ref name="Malone2009">{{cite book|last=Malone|first=John C.|title=Psychology: Pythagoras to present|url=http://books.google.com/books?id=e6Qa6cMQj8AC&pg=PA22|accessdate=25 October 2010|date=30 June 2009|publisher=MIT Press|isbn=978-0-262-01296-6|page=22}}</ref> The Egyptians are said to have taught him geometry, the [[Phoenicia]]ns arithmetic, the [[Chaldea]]ns astronomy, the [[Magi]]ans the principles of religion and practical maxims for the conduct of life.<ref>Porphyry, ''Vit. Pyth.'' 6</ref> Of the various claims regarding his Greek teachers, Pherecydes is mentioned most often.
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Diogenes Laërtius reported that Pythagoras had undertaken extensive travels, having not only visited [[Egypt]] but also "journeyed among the [[Chaldea|Chaldaeans]] and [[Magi]]", for the purpose of collecting all available knowledge and especially to learn information concerning the secret or mystic cults of the gods.<ref>Diogenes Laërtius, viii. 2; Porphyry, ''Vit. Pyth.'' 11, 12; Iamblichus, ''Vit. Pyth.'' 14, etc.</ref> [[Plutarch]] asserted in his book ''[[Moralia|On Isis and Osiris]]'' that during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of
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[[Heliopolis (ancient)|Heliopolis]].<ref>Plutarch, ''[http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/A.html On Isis And Osiris]'', ch. 10.</ref> Other ancient writers asserted his visit to Egypt.<ref>Antiphon. ap. Porphyry, ''Vit. Pyth.'' 7; Isocrates, ''Busiris'', 28–9; Cicero, ''de Finibus'', v. 27; Strabo, xiv.</ref> Enough of Egypt was known to attract the curiosity of an inquiring Greek, and contact between Samos and other parts of Greece with Egypt is mentioned.<ref>Herodotus, ii. 134, 135, iii. 39.</ref>


It is not easy to say how much Pythagoras learned from the Egyptian priests, or indeed, whether he learned anything at all from them. There was nothing in the symbolism which the Pythagoreans adopted which showed the distinct traces of Egypt. The secret religious rites of the Pythagoreans exhibited nothing but what might have been adopted in the spirit of Greek religion, by those who knew nothing of Egyptian mysteries. The philosophy and the institutions of Pythagoras might easily have been developed by a Greek mind exposed to the ordinary influences of the age. Even the ancient authorities note the similarities between the religious and [[ascetic]] peculiarities of Pythagoras with the [[Orphism (religion)|Orphic]] or Cretan [[Greco-Roman mysteries|mysteries]],<ref>Iamblichus, ''Vit. Pyth.'' 25; Porphyry, ''Vit. Pyth.'' 17; Diogenes Laërtius, viii. 3</ref> or the [[Pythia|Delphic oracle]].<ref>Ariston. ap. Diogenes Laërtius, viii. 8, 21; Porphyry, ''Vit. Pyth.'' 41</ref>
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There is little direct evidence as to the kind and amount of knowledge which Pythagoras acquired, or as to his definite philosophical views. Everything of the kind mentioned by [[Plato]] and [[Aristotle]] is attributed not to Pythagoras, but to the Pythagoreans. [[Heraclitus]] stated that he was a man of extensive learning;<ref>Diogenes Laërtius, viii. 6, ix. 1, comp. Herodotus, i. 29, ii. 49, iv. 95</ref> and [[Xenophanes]] claimed that he believed in the [[metempsychosis|transmigration of souls]].<ref>Diogenes Laërtius, viii. 36, comp. Aristotle, ''de Anima'', i. 3; Herodotus, ii. 123.</ref> Xenophanes mentions the story of his interceding on behalf of a [[dog]] that was being beaten, professing to recognise in its cries the voice of a departed friend. Pythagoras is supposed to have claimed that he had been [[Euphorbus]], the son of Panthus, in the [[Trojan war]], as well as various other characters, a tradesman, a courtesan, etc.<ref>Porphyry, ''Vit. Pyth.'' 26; Pausanias, ii. 17; Diogenes Laërtius, viii. 5; Horace, ''Od.'' i. 28,1. 10</ref> In his book ''The Life of Apollonius of Tyana'', [[Philostratus]] wrote that Pythagoras knew not only who he was himself, but also who he had been.<ref>Flavius Philostratus, ''The Life of Apollonius of Tyana '', , trad. F. C. Conybeare, Vol. 2, London, 1912, Book VI, p. 39.</ref>
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Many mathematical and scientific discoveries were attributed to Pythagoras, including [[Pythagorean theorem|his famous theorem]],<ref>Diogenes Laërtius, viii. 12 ; Plutarch, ''Non posse suav. vivi sec. Ep.'' p. 1094</ref> as well as discoveries in the field of [[Music of ancient Greece|music]],<ref>Porphyry, in ''Ptol. Harm.'' p. 213; Diogenes Laërtius, viii. 12</ref> [[Greek astronomy|astronomy]],<ref>Diogenes Laërtius, viii. 14 ; Pliny, ''Hist. Nat.'' ii. 8</ref> and [[Ancient Greek medicine|medicine]].<ref>Diogenes Laërtius, viii. 12, 14, 32</ref> But it was the religious element which made the profoundest impression upon his contemporaries. Thus the people of Croton were supposed to have identified him with the Hyperborean [[Apollo]],<ref>Porphyry, ''Vit. Pyth.'' 20; Iamblichus, ''Vit. Pyth.'' 31, 140; Aelian, ''Varia Historia'', ii. 26; Diogenes Laërtius, viii. 36.</ref> and he was said to have practised [[divination]] and [[prophecy]].<ref>Cicero, ''de Divin.'' i. 3, 46; Porphyry, ''Vit. Pyth.'' 29.</ref> In the visits to various places in Greece – [[Delos]], [[Sparta]], [[Phlius]], [[Crete]], etc. which are ascribed to him, he usually appears either in his religious or priestly guise, or else as a lawgiver.<ref>Iamblichus, ''Vit. Pyth.'' 25; Porphyry, ''Vit. Pyth.'' 17;  Diogenes Laërtius, viii. 3, 13; Cicero, ''Tusc. Qu.'' v. 3</ref>
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[[File:Crotone panorama 2.jpg|right|thumb|Croton on the southern coast of Magna Graecia (Southern Italy), to which Pythagoras ventured after feeling overburdened in Samos.]]
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After his travels, Pythagoras moved (around 530 BC) to [[Crotone|Croton]], in [[Italy]] ([[Magna Graecia]]). Possibly the tyranny of [[Polycrates]] in Samos made it difficult for him to achieve his schemes there. His later admirers claimed that Pythagoras was so overburdened with public duties in Samos, because of the high estimation in which he was held by his fellow-citizens, that he moved to Croton.<ref>Iamblichus, ''Vit. Pyth.'' 28; Porphyry, ''Vit. Pyth.'' 9</ref> On his arrival in Croton, he quickly attained extensive influence, and many people began to follow him. Later biographers tell fantastical stories of the effects of his eloquent speech in leading the people of Croton to abandon their luxurious and corrupt way of life and devote themselves to the purer system which he came to introduce.<ref>Porphyry, ''Vit. Pyth.'' 18; Iamblichus, ''Vit. Pyth.'' 37, etc.</ref>


His followers established a select brotherhood or club for the purpose of pursuing the religious and ascetic practices developed by their master. The accounts agree that what was done and taught among the members was kept a profound secret. The [[esoteric]] teachings may have concerned science and mathematics, or the secret religious doctrines and usages which were undoubtedly prominent in the Pythagorean system, and may have been connected with the worship of Apollo.<ref>Aelian, ''Varia Historia'', ii. 26; Diogenes Laërtius, viii. 13; Iamblichus, ''Vit. Pyth.'' 8, 91, 141</ref> Temperance of all kinds seems to have been strictly urged. There is disagreement among the biographers as to whether Pythagoras forbade all animal food,<ref>as Empedocles did afterwards, Aristotle, ''Rhet.'' i. 14. § 2; Sextus Empiricus, ix. 127. This was also one of the Orphic precepts, Aristoph. ''Ran.'' 1032</ref> or only certain types.<ref>Aristo ap. Diogenes Laërtius, viii. 20; comp. Porphyry, ''Vit. Pyth.'' 7; Iamblichus, ''Vit. Pyth.'' 85, 108</ref> The club was in practice at once "a philosophical school, a religious brotherhood, and a political association."<ref>Thirlwall, ''Hist. of Greece'', vol. ii. p. 148</ref>
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[[File:Pythagoras-Münz.JPG|right|thumb|Pythagoras, depicted on a 3rd-century coin]]
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Such an aristocratic and exclusive club could easily have made many people in Croton jealous and hostile, and this seems to have led to its destruction. The circumstances, however, are uncertain. Conflict seems to have broken out between the towns of [[Sybaris]] and Croton. The forces of Croton were headed by the Pythagorean [[Milo of Croton|Milo]], and it is likely that the members of the brotherhood took a prominent part. After the decisive victory by Croton, a proposal for establishing a more democratic constitution, was unsuccessfully resisted by the Pythagoreans. Their enemies, headed by [[Cylon of Croton|Cylon]] and [[Ninon of Croton|Ninon]], the former of whom is said to have been irritated by his exclusion from the brotherhood, roused the populace against them. An attack was made upon them while assembled either in the house of Milo, or in some other meeting-place. The building was set on fire, and many of the assembled members perished; only the younger and more active escaping.<ref>Iamblichus, ''Vit. Pyth.'' 255–259; Porphyry, ''Vit. Pyth.'' 54–57; Diogenes Laërtius, viii. 39; comp. Plutarch, ''de Gen. Socr.'' p. 583</ref> Similar commotions ensued in the other cities of Magna Graecia in which Pythagorean clubs had been formed.


As an active and organised brotherhood the Pythagorean order was everywhere suppressed, and did not again revive. Still the Pythagoreans continued to exist as a sect, the members of which kept up among themselves their religious observances and scientific pursuits, while individuals, as in the case of [[Archytas]], acquired now and then great political influence. Concerning the fate of Pythagoras himself, the accounts varied. Some say that he perished in the temple with his disciples,<ref>Arnob. ''adv. Gentes'', i. p. 23</ref> others that he fled first to [[Taranto|Tarentum]], and that, being driven from there, he escaped to [[Metapontum]], and there starved himself to death.<ref>Diogenes Laërtius, viii. 39, 40; Porphyry, ''Vit. Pyth.'' 56; Iamblichus, ''Vit. Pyth.'' 249; Plutarch, ''de Stoic. Rep.'' 37</ref> His tomb was shown at Metapontum in the time of [[Cicero]].<ref>Cicero, ''de Fin.'' v. 2</ref>
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According to some accounts Pythagoras married [[Theano (philosopher)|Theano]], a lady of Croton. Their children are variously stated to have included a son, [[Telauges]], and three daughters, [[Damo (philosopher)|Damo]], [[Arignote]], and [[Myia]].
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==Mathematics==
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[[File:Pythagorean.svg|thumb|'''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'').]]
{{Quote|The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.|[[Aristotle]]|''Metaphysics 1–5 '', cc. 350 BC}}


There are good reasons to believe that Pythagoras never dealt with Mathematics ''at all''.<ref>See Burkert's ''Lore and Science in Ancient Pythagoreanism'', Burnyeat's ''Other Lives'', or Machiavelo's ''Pythagoras, Facts and Legends''.</ref> Therefore, although the mathematical ideas exposed below circulated among the Pythagoreans, they may well not be due to Pythagoras himself.
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===Pythagorean theorem===
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{{Main|Pythagorean theorem}}
[[File:Pythag anim.gif|right |thumb|A visual proof of the Pythagorean theorem]]
Since the fourth century AD, Pythagoras has commonly been given credit for discovering the [[Pythagorean theorem]], a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides—that is, <math>a^2 + b^2 = c^2</math>.


While the theorem that now bears his name was known and previously utilized by the [[Babylonian mathematics|Babylonians]] and [[Indian mathematics|Indians]], he, or his students, are often said to have constructed the first proof. It must, however, be stressed that the way in which the Babylonians handled 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.<ref>There are about 100,000 unpublished cuneiform sources in the [[British Museum]] alone. Babylonian knowledge of proof of the Pythagorean Theorem is discussed by J. Høyrup, 'The Pythagorean "Rule" and "Theorem" – Mirror of the Relation between Babylonian and Greek Mathematics,' in: J. Renger (red.): ''Babylon. Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne'' (1999).</ref> Because of the secretive nature of his school and the custom of its students to attribute everything to their teacher, there is no evidence that Pythagoras himself worked on or proved this theorem. For that matter, there is no evidence that he worked on any mathematical or meta-mathematical problems. Some attribute it as a carefully constructed myth by followers of [[Plato]] over two centuries after the death of Pythagoras, mainly to bolster the case for Platonic meta-physics, which resonate well with the ideas they attributed to Pythagoras. This attribution has stuck down the centuries up to modern times.<ref>From Christoph Riedweg , ''Pythagoras, His Life, Teaching and Influence'', Cornell: Cornell University Press, 2005: "Had Pythagoras and his teachings not been since the early Academy overwritten with Plato's philosophy, and had this 'palimpsest' not in the course of the Roman Empire achieved unchallenged authority among Platonists, it would be scarcely conceivable that scholars from the Middle Ages and modernity down to the present would have found the Presocratic charismatic from Samos so fascinating. In fact, as a rule it was the image of Pythagoras elaborated by Neopythagoreans and Neoplatonists that determined the idea of what was Pythagorean over the centuries."</ref> The earliest known mention of Pythagoras's name in connection with the theorem occurred five centuries after his death, in the writings of [[Cicero]] and [[Plutarch]].
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===Musical theories and investigations===
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[[File:Gaffurio Pythagoras.png|thumb|Medieval woodcut showing Pythagoras with bells and other instruments in Pythagorean tuning]]
{{See also|Pythagorean tuning |Pythagorean hammers}}
According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when one day he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how this had happened by looking at their tools, he discovered that it was because the [[Pythagorean hammers|hammers]] were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on."


This legend has since proven to be false by virtue of the fact that these ratios are only relevant to string length (such as the string of a [[monochord]]), and not to hammer weight.<ref>Weiss, Piero, and Richard Taruskin, eds. Music in the Western World: A History in Documents. 2nd ed. N.p.: Thomson Schirmer, 1984. 3. Print.</ref><ref>[http://books.google.com/books?id=ioa9uW2t7AQC&pg=PA143&lpg=PA143&dq=pythagoras+hammers+myth&source=bl&ots=wtLXShWfVQ&sig=LlyPLjIoE0O25ieAj9-2h7J1Qq8&hl=en&ei=itsgTduSB8L7lwf6os3UCw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCoQ6AEwAw#v=onepage&q=pythagoras%20hammers%20myth&f=false Christensen, Thomas, ed. The Cambridge history of Western music theory. Cambridge: Cambridge University Press, 2002. 143. Print.]</ref> However, it may be that Pythagoras was indeed responsible for discovering these properties of string length.
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Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Another belief attributed to Pythagoras was that of the "[[Musica universalis|harmony of the spheres]]". Thus the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony.<ref>Christoph Riedweg, Pythagoras: His Life, Teaching and Influence, Cornell: Cornell University Press, 2005 .</ref>
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Pythagoras was also credited with devising the [[tetractys]], the triangular figure of four rows, which add up to the perfect number, ten. As a mystical symbol, it was very important to the worship of the Pythagoreans, who would swear oaths by it:
 
{{quote|And the inventions were so admirable, and so divinised by those who understood them, that the members used them as forms of oath: "By him who handed to our generation the ''tetractys'', source of the roots of ever-flowing nature."|Iamblichus, ''Vit. Pyth.'', 29}}
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==Religion and science==
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Pythagoras' religious and scientific views were, in his opinion, inseparably interconnected. Religiously, Pythagoras was a believer of [[metempsychosis]]. He believed in [[Transmigration of the soul|transmigration]], or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables until it became immortal. His ideas of reincarnation were influenced by ancient Greek religion. [[Heraclides Ponticus]] reports the story that Pythagoras claimed that he had lived four previous lives that he could remember in detail.<ref>Diogenes Laërtius, viii. 3–4</ref> One of his past lives, as reported by [[Aulus Gellius]], was as a beautiful courtesan.<ref>Aulus Gellius, iv. 11</ref> According to [[Xenophanes]], Pythagoras heard the cry of his dead friend in the bark of a dog.<ref>Diogenes Laërtius, viii. 36</ref>


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Pythagoras became the subject of elaborate legends surrounding his historic persona. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure, attributing to him such aspects as a golden thigh, which was a sign of divinity. According to [[Hermes Trismegistus#In Islamic tradition|Muslim tradition]], Pythagoras was said to have been initiated by [[Hermes Trismegistus|Hermes]] (Egyptian [[Thoth]]).<ref>See Antoine Faivre, in ''The Eternal Hermes'' (1995)</ref> According to Aristotle and others' accounts, some ancients believed that he had the ability to travel through space and time, and to communicate with animals and plants.<ref>[http://plato.stanford.edu/entries/pythagoras/#PytWon Huffman, Carl. Pythagoras (Stanford Encyclopedia of Philosophy)]</ref> An extract from [[Brewer's Dictionary of Phrase and Fable]]'s entry entitled "Golden Thigh":<blockquote>
 
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Another legend describes his writing on the moon:
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<blockquote>''Pythagoras asserted he could write on the moon. His plan of operation was to write on a looking-glass in blood, and place it opposite the moon, when the inscription would appear photographed or reflected on the moon's disc.''<ref>[http://www.infoplease.com/dictionary/brewers/pythagoras.html Brewer, E. Cobham, ''Brewer's Dictionary of Phrase and Fable'']</ref></blockquote>


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{{See also|Pythagoreanism}}
 
[[File:Sanzio 01 Pythagoras.jpg|thumb|Pythagoras, the man in the center with the book, teaching music, in [[The School of Athens]] by [[Raphael]]]]
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Both [[Plato]] and [[Isocrates]] affirm that, above all else, Pythagoras was famous for leaving behind him a way of life.<ref>Plato, ''Republic'', 600a, Isocrates, ''Busiris'', 28</ref> Both [[Iamblichus]] and [[Porphyry (philosopher)|Porphyry]] give detailed accounts of the organisation of the school, although the primary interest of both writers is not historical accuracy, but rather to present Pythagoras as a divine figure, sent by the [[Greek gods|gods]] to benefit humankind.<ref>John Dillon and Jackson Hershbell, (1991), ''Iamblichus, On the Pythagorean Way of Life'', page 14. Scholars Press.; D. J. O'Meara, (1989), ''Pythagoras Revived. Mathematics and Philosophy in Late Antiquity'', pages 35–40. Clarendon Press.</ref>
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Pythagoras set up an organization which was in some ways a school, in some ways a brotherhood (and here it should be noted that sources indicate that as well as men there were many women among the adherents of Pythagoras),<ref>Porphyry, ''Vit. Pyth.'' 19</ref> and in some ways a monastery. It was based upon the religious teachings of Pythagoras and was very secretive. The adherents were bound by a [[vow]] to Pythagoras and each other, for the purpose of pursuing the [[religious]] and [[ascetic]] observances, and of studying his religious and [[philosophical]] theories. The claim that they put all their property into a common stock is perhaps only a later inference from certain Pythagorean maxims and practices.<ref>comp. Cicero, ''de Leg.'' i. 12, ''de Off.'' i. 7; Diogenes Laërtius, viii. 10</ref>
You can download available titles to only two separate devices at one time. If you have already downloaded a title to two devices, you need to delete it in one of them before downloading it to a different device. While not all Prime [http://www.ngs.com.sg/publish/backup.asp Abercrombie And Fitch Malaysia] Instant Video titles are for sale to download, the same videos might be available for rental or obtain Amazon Instant Video, and rented or purchased titles obtainable to compatible devices.Viewing Period: If you have a Prime membership or Prime free trial, you can stream any video that's currently designated as a Prime Instant Video title on its detail page. <br><br>Ambati Thirupathi Rayudu (born September 23, 1985 in Guntur, Andhra Pradesh), is a former Indian first class [http://www.heritagepress.co.nz/config/links.php Oakley Nz] cricketer. He is a righthanded batsman and a rightarm offbreak bowler. He is currently an ICL player. Rayudu is a middle order batsman, making his debut in Ranji Trophy domestic cricket in the 2001/02 cricket season for Hyderabad. In the 2002/03 season, Rayudu designed a double century and a century in a match against Andhra Pradesh. He played for his home state, Andhra Pradesh, for one season (2005/2006). He currently represents the Hyderabad team in Indian domestic cricket. Rayudu was selected to represent the India Under19 cricket team in the 2002 tour of England. Within the third One Day International, Rayudu scored 177, helping his side to overhaul England\'s total of 305. In the last match he had performed a similar role when his 80 laid the building blocks for a victorious runchase as the Indians defeated their English counterparts 30 in the ODI series. In the 2004/2005 threetest series against England Under19, he scored three consecutive halfcenturies. Rayudu captained India Under19 in the 2003/2004 Under19 Cricket World Cup. He seemed to be a regular in the India A squad. Find out more ><br><br>Americans for Safe Access, NORML, CAMP 420 and many others can be seen fighting for patients rights in Arizona and would now appear you can include the previously reclusive Hayes to the list of outspoken advocates for Arizona's medical marijuana patients. The site listed as the "home page" is currently [http://www.ec-link.com/event/media.asp Nike Cortez] the No 25 Mile Rule Arizona Facebook page with no contact phone number is available at the moment. <br><br>Many website monitoring services offer communication via email. Sometimes this just isn't enough. What if your email server [http://www.environmentalarts.co.nz/temp/list.php Insanity Asylum] falls with your site? Then you will not be notified of the outage until your internet site is back up and running again since you won't receive the email. Be sure you utilize a website monitor that communicates via SMS text and phone in addition to email. This can ensure that you know when your site falls, regardless of whether or not your email server goes down with it.<ul>
 
 
As to the internal arrangements of the sect, we are informed that what was done and taught among the members was kept a profound [[secret]] towards all. Porphyry stated that this silence was "of no ordinary kind." Candidates had to pass through a period of probation, in which their powers of maintaining silence (''echemythia'') were especially tested, as well as their general temper, disposition, and mental capacity.<ref>Aristonexus ap. Iamblichus, ''Vit. Pyth.'' 94</ref> There were also gradations among the members themselves. It was an old Pythagorean maxim, that every thing was not to be told to every body.<ref>Diogenes Laërtius, viii. 15; Aristonexus ap. Iamblichus, ''Vit. Pyth.'' 31</ref> Thus the Pythagoreans were divided into an inner circle called the ''mathematikoi'' ("learners") and an outer circle called the ''akousmatikoi'' ("listeners").<ref>Iamblichus, ''Vit. Pyth.'' 80, cf. Aulus Gellius, i. 9</ref> Iamblichus describes them in terms of ''esoterikoi'' and ''exoterikoi'' (or alternatively ''Pythagoreioi'' and ''Pythagoristai''),<ref>Iamblichus, ''Vit. Pyth.'' 80</ref> according to the degree of intimacy which they enjoyed with Pythagoras. Porphyry wrote "the ''mathematikoi'' learned the more detailed and exactly elaborated version of this knowledge, the ''akousmatikoi'' (were) those who had heard only the summary headings of his (Pythagoras's) writings, without the more exact exposition."
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There were [[ascetic]] practices (many of which had, perhaps, a symbolic meaning) in the way of life of the sect.<ref>comp. Porphyry, ''Vit. Pyth.'' 32; Iamblichus, ''Vit. Pyth.'' 96, etc.</ref> Some represent Pythagoras as forbidding all animal food, advocating a plant-based diet, and prohibiting consumption of beans. This may have been due to the doctrine of [[metempsychosis]].<ref>Plutarch, ''de Esu Carn.'' pp. 993, 996, 997</ref> Other authorities contradict the statement. According to [[Aristoxenus]],<ref>Aristoxenus ap. Diogenes Laërtius, viii. 20</ref> he allowed the use of all kinds of animal food except the flesh of [[oxen]] used for [[plough]]ing, and [[sheep|rams]].<ref>comp. Porphyry, ''Vit. Pyth.'' 7; Iamblichus, ''Vit. Pyth.'' 85, 108</ref> There is a similar discrepancy as to the prohibition of [[fish]] and [[beans]].<ref>Diogenes Laërtius, viii. 19, 34; Aulus Gellius, iv. 11; Porphyry, ''Vit. Pyth.'' 34, ''de Abst.'' i. 26; Iamblichus, ''Vit. Pyth.'' 98</ref> But temperance of all kinds seems to have been urged. It is also stated that they had common meals, resembling the [[Sparta]]n system, at which they met in companies of ten.<ref>Iamblichus, ''Vit. Pyth.'' 98; Strabo, vi.</ref>
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Considerable importance seems to have been attached to [[music]] and [[gymnastics]] in the daily exercises of the disciples. Their whole discipline is represented as encouraging a lofty serenity and self-possession, of which, there were various anecdotes in antiquity.<ref>Athenaeus, xiv. 623; Aelian, ''Varia Historia'', xiv. 18; Iamblichus, ''Vit. Pyth.'' 197</ref> Iamblichus (apparently on the authority of [[Aristoxenus]])<ref>Iamblichus, ''Vit. Pyth.'' 96–101</ref> gives a long description of the daily routine of the members, which suggests many similarities with Sparta. The members of the sect showed a devoted attachment to each other, to the exclusion of those who did not belong to their ranks.<ref>Aristonexus ap. Iamblichus, ''Vit. Pyth.'' 94, 101, etc., 229, etc.; comp. the story of Damon and Phintias; Porphyry, ''Vit. Pyth.'' 60; Iamblichus, ''Vit. Pyth.'' 233, etc.</ref> There were even stories of secret symbols, by which members of the sect could recognise each other, even if they had never met before.<ref>Scholion ad Aristophanes, ''Nub.'' 611; Iamblichus, ''Vit. Pyth.'' 237, 238</ref>
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==Influence==
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===Influence on Plato===
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[[File:Nuremberg chronicles f 61v 2.png|right|thumb|Pythagoras, depicted as a medieval scholar in the ''[[Nuremberg Chronicle]]'']]
 
Pythagoras, or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of [[Plato]]. According to [[R. M. Hare]], this influence consists of three points: (1) The [[Republic (Plato)|platonic Republic]] might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton. (2) There is evidence that Plato possibly took from Pythagoras the idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for substantial theses in [[science]] and [[morals]]". (3) Plato and Pythagoras shared a "mystical approach to the [[Soul (spirit)|soul]] and its place in the material world". It is probable that both were influenced by [[Orphicism|Orphism]].<ref>R.M. Hare, Plato in C.C.W. Taylor, R.M. Hare and Jonathan Barnes, Greek Philosophers, Socrates, Plato, and Aristotle, Oxford: Oxford University Press, 1999 (1982), 103–189, here 117–9.</ref>
</ul>
 
Aristotle claimed that the philosophy of Plato closely followed the teachings of the Pythagoreans,<ref>Metaphysics, 1.6.1 (987a)</ref> and Cicero repeats this claim: ''Platonem ferunt didicisse Pythagorea omnia'' ("They say Plato learned all things Pythagorean").<ref>Tusc. Disput. 1.17.39.</ref> [[Bertrand Russell]], in his ''[[A History of Western Philosophy]]'', contended that the influence of Pythagoras on Plato and others was so great that he should be considered the most influential of all Western philosophers.
 
===Politics and science===
 
Pythagoras was the first person known to have taught the earth was spherical, with [[antipodes]] and that it revolved around the sun. Pythagoras was also said to have spread the seeds of political liberty to Crotona, Sybaris, Meapontum, Rhegium, Sicily, Tauromenium, Catana, Agrigentum and Himera.<ref>{{cite web|url=https://archive.org/details/livesnecromance04godwgoog|title=Lives of the Necromancers|author=William Godwin|year=1876|page=48}}</ref>
 
===Influence on esoteric groups===
Pythagoras started a secret society called the ''Pythagorean Brotherhood'' devoted to the study of mathematics. This had a great effect on future esoteric traditions, such as [[Freemasonry]] and [[Rosicrucianism]], both of which were scientific/mystical groups dedicated to the study of mathematics/[[geometry]] and logical reasoning as opposed to religious dogma. Both Freemasonry and Rosicrucianism have claimed to have evolved out of the Pythagorean Brotherhood. The mystical and occult qualities of Pythagorean mathematics are discussed in a chapter of Manly P. Hall's ''The Secret Teachings of All Ages'' entitled "Pythagorean Mathematics".<ref>Hall, Manly ''The Secrets Teaching of All Ages'' Tarcher Penguin 2003 pages 191–221.</ref>
 
==See also==
{{col-begin}}
{{col-2}}
*[[Apollonius of Tyana]]
*[[Dyad (Greek philosophy)]]
*''[[The golden verses of Pythagoras]]''
*[[Isopsephy]] ([[Gematria]])
*[[List of things named after Pythagoras]]
*[[Lute of Pythagoras]]
{{col-break}}
*[[Neopythagoreanism]]
*[[Pythagoras tree (fractal)]]
*[[Pythagorean comma]]
*[[Pythagorean cup]]
*[[Pythagorean triple]]
*[[Sacred geometry]]
{{col-end}}
 
==References==
{{Reflist|colwidth=30em}}
 
==Sources==
 
===Classical secondary sources===
<div class="references-small">
Only a few relevant source texts deal with Pythagoras and the Pythagoreans, most are available in different translations. Other texts usually build solely on information in these works.
 
*[[Diogenes Laërtius]], ''[[Lives and Opinions of Eminent Philosophers|Vitae philosophorum VIII]]'' (''Lives of Eminent Philosophers''), c. 200 AD, which in turn references the [[lost work]] ''[[Successions of Philosophers]]'' by [[Alexander Polyhistor]] &mdash; {{ws|[[s:Lives of the Eminent Philosophers/Book VIII#Pythagoras|''Life of Pythagoras'']], translated by [[Robert Drew Hicks]] (1925)}}
*[[Porphyry (philosopher)|Porphyry]], ''Vita Pythagorae'' (''Life of Pythagoras''), c. 270 AD &mdash; [http://www.ccel.org/ccel/pearse/morefathers/files/porphyry_life_of_pythagoras_02_text.htm ''Porphyry, Life of Pythagoras''], translated by [[Kenneth Sylvan Guthrie]] (1920)
*[[Iamblichus (philosopher)|Iamblichus]], ''De Vita Pythagorica'' (''On the Pythagorean Life''), c. 300 AD &mdash; [http://www.completepythagoras.net/mainframeset.html ''Iamblichus, Life of Pythagoras''], translated by [[Kenneth Sylvan Guthrie]] (1920)
*[[Apuleius]] also writes about Pythagoras in ''Apologia'', c. 150 AD, including a story of him being taught by [[Babylon]]ian disciples of [[Zoroaster]]
*[[Hierocles of Alexandria]], ''Golden Verses of Pythagoras'', c. 430 AD
</div>
 
===Modern secondary sources===
<div class="references-small">
*[[Walter Burkert|Burkert, Walter]]. ''Lore and Science in Ancient Pythagoreanism''. Harvard University Press, June 1, 1972. ISBN 0-674-53918-4
*[[Myles Burnyeat|Burnyeat, M. F.]] [http://www.lrb.co.uk/v29/n04/burn02_.html "Other Lives"]. ''London Review of Books'', 22 February 2007.
*Guthrie, W. K. ''A History of Greek Philosophy: Earlier Presocratics and the Pythagoreans'', Cambridge University Press, 1979. ISBN 0-521-29420-7
*[[Peter Kingsley (scholar)|Kingsley, Peter]]. ''Ancient Philosophy, Mystery, and Magic: Empedocles and the Pythagorean Tradition''. Oxford University Press, 1995.
*[[Arnold Hermann|Hermann, Arnold]]. ''To Think Like God: Pythagoras and Parmenides—the Origins of Philosophy''. Parmenides Publishing, 2005. ISBN 978-1-930972-00-1
*{{Cite journal|last1 = Machiavelo|first1 = António|year = 2009|title = Pythagoras, Facts and Legends|journal = EMS Newsletter|issue = 74|pages = 25–26|publisher = [[European Mathematical Society]]|url = http://www.mathematics-in-europe.eu/images/information_pdf/hist_phil_pdf/hist_pdf/machiavelo.pdf|accessdate = 25 September 2013}}
*O'Meara, Dominic J. ''Pythagoras Revived''. Oxford University Press, 1989. ISBN 0-19-823913-0 (paperback), ISBN 0-19-824485-1 (hardcover)
</div>
 
==External links==
{{wikiquote}}
{{Commons category}}
{{Wikisource1911Enc|Pythagoras}}
*{{In Our Time|Pythagoras|b00p693b|Pythagoras}}
*{{sep entry|pythagoras|Pythagoras|Carl Huffman}}
*[http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Pythagoras.html ''Pythagoras of Samos''], The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland
*[http://history.hanover.edu/texts/presoc/pythagor.html ''Pythagoras and the Pythagoreans, Fragments and Commentary''], Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History
*[http://www.math.tamu.edu/~don.allen/history/pythag/pythag.html ''Pythagoras and the Pythagoreans''], Department of Mathematics, Texas A&M University
*[http://www.newadvent.org/cathen/12587b.htm ''Pythagoras and Pythagoreanism''], The Catholic Encyclopedia
*[http://www.organelle.org/organelle/tetra/tetraktys.html ''Tetraktys'']
*[http://pythagoras.name/golden_verses_of_pythagoras.html ''Golden Verses of Pythagoras'']
*[http://www.animalrightshistory.org/animal-rights-antiquity/pythagoras.htm ''Pythagoras on Vegetarianism''] Quotes from  primary source historical literature on Pythagoras' view on Vegetarianism, Justice and Kindness
*[http://users.ucom.net/~vegan/ ''Homage to Pythagoras'']
*[http://web.archive.org/web/20091027110142/http://geocities.com/go_darkness/god-pythagorean-pentacle.html ''Occult conception of Pythagoreanism'']
*[http://cyberspacei.com/jesusi/inlight/philosophy/western/Pythagoreanism.htm ''Pythagoreanism Web Article'']
*[http://luchte.wordpress.com/wandering-souls-the-doctrine-of-transmigration-in-pythagorean-philosophy/ ''Wandering Souls: The Doctrine of Transmigration in Pythagorean Philosophy''], by Dr. James Luchte
*[http://freedocumentaries.net/media/164/Pythagoras/ 45-minute documentary] about Pythagoras
*[http://www.regolish.com/Plays.htm Io and Pi – theatrical play on Pythagoras' life]
*The [http://www.sacred-texts.com/cla/gvp/gvp11.htm Symbols] of Pythagoras at The Sacred Texts online
*[http://demonax.info/doku.php?id=archaic:pythagoras Pythagorean Texts]
 
{{Greek mathematics}}
{{Presocratics}}
{{Greek schools of philosophy}}
{{Ancient Greece topics}}
 
{{Authority control|VIAF=100220077|LCCN=n/80/162846}}
 
<!-- Metadata: see [[Wikipedia:Persondata]] -->
{{Persondata
|NAME= Pythagoras
|ALTERNATIVE NAMES=Πυθαγόρας (Greek)
|SHORT DESCRIPTION=Ionian philosopher
|DATE OF BIRTH=circa 570 BC
|PLACE OF BIRTH=[[Samos]]
|DATE OF DEATH=circa 495 BC
|PLACE OF DEATH= [[Metapontum]]
}}
[[Category:Pythagoras| ]]
[[Category:6th-century BC births]]
[[Category:5th-century BC deaths]]
[[Category:6th-century BC Greek people]]
[[Category:6th-century BC philosophers]]
[[Category:Ancient Greek mathematicians]]
[[Category:Ancient Greek music theorists]]
[[Category:Ancient Greek philosophers]]
[[Category:Ancient Greek political refugees]]
[[Category:Ancient Greek shamans]]
[[Category:Ancient Samians]]
[[Category:Ascetics]]
[[Category:Esotericists]]
[[Category:Founders of religions]]
[[Category:Geodesists]]
[[Category:Geometers]]
[[Category:Mystics]]
[[Category:Numerology]]
[[Category:Philosophy of mathematics]]
[[Category:Philosophy of music]]
[[Category:Physiognomists]]
[[Category:Pythagoreans| ]]
 
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Latest revision as of 16:35, 2 December 2014

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