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| | Pythagoras - Wikipedia, the free encyclopedia |
 | | Today, Pythagoras is revered as a prophet by the Ahlu l-Tawhīd or Druze faith along with his fellow Greek, Plato. | | | Pythagoras undertook a reform of the cultural life of Crotone, urging the citizens to follow virtue and form an elite circle of followers around himself. | | | In his biography of Pythagoras (written seven centuries after Pythagoras's time) Porphyry stated that this silence was "of no ordinary kind." The Pythagoreans were divided into an inner circle called the mathematikoi ("mathematicians") and an outer circle called the akousmatikoi ("listeners"). |
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http://en.wikipedia.org/wiki/Pythagoras
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| | Pythagoras and the Pythagoreans |
| | Pythagoras held that one of the first principles, the monad, is god and the good, which is the origin of the One, and is itself intelligence; but the undefined dyad is a divinity and the bad, surrounding which is the mass of matter. | | | Pythagoras laid down [Page 155] the doctrine of the monad and of foreknowledge and the interdict on sacrificing to the gods then believed on, and he bade men not to partake of beings that had life, and to refrain from wine. | | | Pythagoras said that this sacred tetraktys is 'the spring having the roots of ever-flowing nature in itself, and from this numbers have their first principle. |
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http://history.hanover.edu/texts/presoc/pythagor.htm
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| | Pythagoras [Internet Encyclopedia of Philosophy] |
| | Originally from Samos, Pythagoras founded at Kroton (in southern Italy) a society which was at once a religious community and a scientific school. | | | It was natural for Pythagoras to look for something of the same kind in the world at large. | | | That is the great contribution of Pythagoras to philosophy, and we must try to understand it. |
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http://www.utm.edu/research/iep/p/pythagor.htm
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| | Pythagoras |
| | In the modern world Pythagoras is most of all famous as a mathematician, because of the theorem named after him, and secondarily as a cosmologist, because of the striking view of a universe ascribed to him in the later tradition, in which the heavenly bodies produce “the music of the spheres” by their movements. | | | Porphyry also emphasizes Pythagoras' divine aspects and may be setting him up as a rival to Jesus (Iamblichus 1991, 14). | | | Sources above, the following account of Pythagoras' philosophy is based in the first place on the evidence prior to Aristotle and in the second place on evidence that our sources explicitly identify as deriving from Aristotle's books on the Pythagoreans as well as from the books of his pupils such as Aristoxenus and Dicaearchus. |
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http://plato.stanford.edu/entries/pythagoras
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| | Pythagoras, Phoenician/Greek Mathematician |
| | Pythagoras was refused admission to all the temples except the one at Diospolis where he was accepted into the priesthood after completing the rites necessary for admission. | | | Pythagoras founded a philosophical and religious school in Croton (now Crotone, on the east of the heel of southern Italy) that had many followers. | | | We do have details of Pythagoras's life from early biographies which use important original sources yet are written by authors who attribute divine powers to him, and whose aim was to present him as a god-like figure. |
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http://phoenicia.org/pythagoras.html
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| | TMTh:: PYTHAGORAS |
| | Pythagoras soon left the island of his birth for Croton, in south Italy, where with a community of friends he founded a religious brotherhood and school. | | | He held that the substance of all things was number, and that the Universe came forth out of chaos, through measure and harmony acquiring form: Pythagoras, indeed, was the first to call the universe the "cosmos", meaning "the harmonious order of things". | | | He is also said to have been seen talking with his disciples "on the same day and at the selfsame hour" in Metapontum and in Croton. |
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http://www.tmth.edu.gr/en/aet/1/85.html
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| | Pythagoras of Samos, Mathematician, Philosopher and Boxer |
| | Pythagoras taught that science, was revealed to men by "celestial deities," those godlike men who were the Divine Instructors of the Third Race. | | | Thaletes made Pythagoras sail to Egypt and meet with the priests at Memphis and Diospolis, because they had been the ones who had instructed him in those disciplines, through which he was called a learned man among the people. | | | Pythagoras began his talks always saying: “No, by the air I am breathing, no by the water I am drinking I do not allow any contradiction to what I say.” He talked with animals. |
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http://www.mlahanas.de/Greeks/PythagorasStar.htm
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| | Pythagoras |
| | Although Pythagoras arrived in India too late to come into personal contact with the Buddha, he was greatly influenced by his teachings. | | | In the first quarter of the sixth century B.C. he and his wife Parthenis went to Delphi to consult the Oracle, who told Parthenis that she would bear a son who would surpass all men in wisdom and virtue. | | | Instead of being welcomed by his countrymen, Pythagoras found them indifferent to the wisdom he was so eager to impart. |
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http://www.wisdomworld.org/additional/ancientlandmarks/Pythagoras.html
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| | Diogenes Laertius, Life of Pythagoras, from Lives of the Philosophers, translated by C.D. Yonge |
| | And they, being charmed by what he told them, wept and lamented, and believed that Pythagoras was a divine being; so that they even entrusted their wives to him, as likely to learn some good from him; and that they too were called Pythagoreans. | | | Diogenes, is wrong however, in calling him a disciple of Pythagoras (see Bentley on Phalaris), as he lived about a hundred years before his time; his true date being 660 B.C. The code of Zaleucus is stated to have been the first collection of written laws that the Greeks possessed. | | | He is said to have been a man of the most dignified appearance, and his disciples adopted an opinion respecting him, that he was Apollo who had come from the Hyperboreans; and it is said, that once when he was stripped naked, he was seen to have a golden thigh. |
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http://classicpersuasion.org/pw/diogenes/dlpythagoras.htm
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| | Pythagoras was a Greek philosopher, born on the island of Samos |
| | It is believed the Pythagoras and his followers were vegetarians. | | | Pythagoras believed that the letters in the alphabet corresponded to certain numbers. | | | His most important belief was the belief that the earth was in motion. |
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http://www.simplynumbers.com/html/tutor/pythagoras.asp
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| | Greek Philosophers and Aristophanes by Sanderson Beck |
| | Pythagoras taught that all life is akin, and so he believed in universal friendship; he did not worship at altars where animals were sacrificed. | | | Pythagoras carried on the teachings of the Orphic mysteries as well as those of the Egyptian priests. | | | Pythagoras lived during that sixth century BC which gave so many inspired religious leaders to humanity. |
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http://www.san.beck.org/GPJ4-GreekPhilosophers.html
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| | pythagoras |
| | This movement of his, known as the Pythagoreans, was almost like a religion were the numbers were regarded as gods. | | | Pythagoras himself said that he had once before lived as a warrior in the Troja-war. | | | Despite of him being there, Pythagoras tried to found a school there. |
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http://home.c2i.net/greaker/comenius/9899/pythagoras/pythagoras.html
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| | fUSION Anomaly. Pythagoras |
| | Members of the order regarded Pythagoras as a demigod and attributed all their doctrines to him. | | | Egypt to learn from that country's fabled temple priests; there he remained for twenty-two years. | | | Egyptian doctrine, requested his disciples to reject the judgment of their ears as susceptible to error and variation where |
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http://fusionanomaly.net/pythagoras.html
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| | Pythagoras and the Pythagoreans |
| | The school of Pythagoras was every bit as much a religion as a school of mathematics. | | | The whole concept of an eternal world revealed to intellect but not to the senses can be attributed from the teachings of Pythagoras. | | | The school of Pythagoras represents the mystic tradition in contrast with the scientific!! |
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http://www.math.tamu.edu/~dallen/history/pythag/pythag.html
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| | Pythagorean History |
| | The group was almost cult-like in that it had symbols, rituals and prayers. | | | Not much more is known of his early years. | | | These numerical values, in turn, were endowed with mystical and spiritual qualities. |
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http://www.geom.uiuc.edu/~demo5337/Group3/hist.html
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| | PYTHAGORAS the mathemagician |
| | You will sleep in this sarcophagus for three days and three nights, Pythagoras, and wait for the light of Osiris." The High Priest uttered mystically and it vibrated in the Chamber. | | | They brought two children to life, who later continued the mission of their father. | | | A great magnetic light was diffused into the realm of darkness. |
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http://el-koussa.zgharta.com/el-koussa/books/pythagoras.htm
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| | Number and the Cosmos |
| | Pythagoras believed that the universe was formed by the harmonies of the Limited and the Indefinite, Form and Matter, and other such opposites. | | | It was divine and universal, and its reach went beyond the physical dimensions into the sacred dimension of the mind. | | | The following are among the Pythagorean doctrines taught at his school: |
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http://www.astronomy.pomona.edu/archeo/greece/pythagoras/ideas.htm
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| | Webquest.Pythagoras |
| | What were the members of Pythagoras' Philosophical and Religious School expected to do? | | | The theorem can only be used with triangles, true or false. | | | You may answer the following questions by searching the internet or by clicking here: |
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http://edweb.sdsu.edu/T2arp/quest/pythagoras.webquest/webquest.pythagoras.html
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| | Harmony and Proportion: Pythagoras: Music and Space |
| | Pythagoras (6th century BC) observed that when the blacksmith struck his anvil, different notes were produced according to the weight of the hammer. | | | Together with its underlying mathematical laws of proportion it is the sound of the harmony of the created being of the universe, the harmony of what Plato called the "one visible living being, containing within itself all living beings of the same natural order". | | | Pythagoras taught that each of the seven planets produced by its orbit a particular note according to its distance from the still centre which was the Earth. |
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http://www.aboutscotland.com/harmony/prop.html
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| | Pythagoras and Irrational Numbers |
| | But calling Pythagoras a "pure mathematician" is not really the whole truth, as his beliefs and teachings did not deal entirely with pure math in the modern sense, which includes the idea of pure math being completely abstract from the real world. | | | He had two groups of students, the mathematikoi, who were strict followers of everything Pythagoras believed in, including vegetarianism and monk-like purity of life, and the akousmatics, who came to the school from their own homes and lived like regular Greeks when they weren't there studying (O'Conner). | | | reality, at its deepest level, is mathematical in nature; that philosophy can be used for spiritual purification; that the soul can rise to union with the divine; and that certain symbols have a mystical significance, ("Pythagoras" - Britannica) |
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http://community.middlebury.edu/~dwalker/class/godelpaper1.htm
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| | Pythagorean Theorem |
| | Pythagoras lived during the 6th century B.C. on the island of Samos in the Aegean Sea. | | | The relationship was shown on a 4000 year old Babylonian tablet now known as Plimpton 322. | | | Pythagoras found out that for a right angle triangle (with one of the angles being 90 |
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http://www.cs.ucla.edu/~klinger/dorene/math1.htm
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| | Some Pythagorean Texts |
| | Pythagoras seems to have been the first to bring these beliefs into Greece." | | | All Greeks and all barbarians alike count up to ten, and having reached ten revert again to the unity. | | | What he says about Pythagoras runs thus: Once they say that he was passing by when a puppy was being whipped, and he took pity and said, `Stop, do not beat it. |
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http://www.csun.edu/~hcfll004/pythag.html
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| | Pythagoras |
| | Pythagoras believed that 1 is the source of all numbers. | | | The soul is an eternal, self-moving number which passes from body to body. | | | Pythagoras revealed many mathematical truths and profound relationships are continuing to be discovered. |
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http://www.geocities.com/apollonius_theocritos/Pythagoras.htm
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| | Pythagoras |
| | Pythagoras was a Greek philosopher who lived between 580-520 B.C. He believed that everything was related to mathematics and once said "all is number". | | | Pythagoras was a Greek philosopher who lived between 580-520 B.C. He founded a philosophical and religious school in Croton, which made outstanding contributions to the field of mathematics. | | | Pythagoras is also famous for his study of acoustics and his theorem relating the lengths of the sides of a right triangle, which confirmed the existence of irrational numbers. |
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http://www.windows.ucar.edu/people/ancient_epoch/pythagoras.html
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| | Pythagorean theorem - Wikipedia, the free encyclopedia |
| | Van der Waerden believes that "it was certainly based on earlier traditions". | | | More recently, Shri Bharati Krishna Tirthaji in his book[5] claimed ancient Indian Hindu Vedic proofs for the Pythagoras Theorem. | | | According to Sir Thomas L. Heath, there is no attribution of the theorem to Pythagoras for five centuries after Pythagoras lived. |
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http://en.wikipedia.org/wiki/Pythagorean_theorem
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| | Pythagoras |
| | Pythagorean centers sprang up throughout the Greek mainland during the 5th century bce, including in Thebes and Athens, so he certainly influenced Socrates and therefore Plato. | | | Pythagoras believed in reincarnation and claimed to remember previous incarnations. | | | The stories are intended to inspire respect for the wonders of nature (however based in speciesistic assumptions that stories must be about humans). |
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http://www.wsu.edu/~delahoyd/pythagoras.html
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| | Amazon.com: Pythagoras' Trousers: God, Physics, and the Gender Wars: Books: Margaret Wertheim |
| | In the book Pythagoras' Trousers - God, Physics, and the Gender Wars, Margaret Wertheim makes the case that, in its origins, physics was intimately connected with religion. | | | Pythagoras studied mathematics with the Babylonians and began the theory that numbers were divine. | | | I also lent it to my mom who was drawn to the "God" part of the title. |
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http://www.amazon.com/exec/obidos/tg/detail/-/0393317242?v=glance
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| | Pythagoras. The Columbia Encyclopedia, Sixth Edition. 2001-05 |
| | The believers performed purification rites and followed moral, ascetic, and dietary rules to enable their souls to achieve a higher rank in their subsequent lives and thus eventually be liberated from the “wheel of birth.” This belief also led them to regard the sexes as equal, to treat slaves humanely, and to respect animals. | | | The highest purification was “philosophy,” and tradition credits Pythagoras with the first use of the term. | | | Beginning with the discovery that the relationship between musical notes could be expressed in numerical ratios (see Greek music), the Pythagoreans elaborated a theory of numbers, the exact meaning of which is still disputed by scholars. |
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http://www.bartleby.com/65/py/Pythagor.html
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| | Biography of Pythagoras |
| | Pythagoras believed all of these heavenly bodies moving created a "Harmony of Spheres." | | | Pythagoras is one of the great thinkers of his time. | | | Pythagoras believed in secrecy and communalism, so distinguishing his work from the work of his followers is almost impossible. |
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http://www.andrews.edu/~calkins/math/biograph/biopytha.htm
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| | Mathematics & Music |
| | Even though he apparently conviced everybody that the world is a sphere, for some reason he is best known for the infamous theorum below regarding triangles: | | | Pythagoras is a Greek mathematician from the 6 | | | Pythagoras and his contemporary acousticians/musicians/mathematicians believed that the most consonant interval was a unison (i.e. |
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http://www.davesabine.com/music/mathematics.asp?action=pythagoras
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| | CATHOLIC ENCYCLOPEDIA: Pythagoras and Pythagoreanism |
| | he subsequent elaboration of these three central doctrines into a complicated system is the work of the followers of Pythagoras. | | | Naturally, as soon as the legends began to grow up around the name of Pythagoras, many tenets were ascribed him which were in fact introduced by later Pythagoreans, such as Philolaus and Archytas of Tarentum. | | | Aristotelianism, which reduced philosophy to knowledge, never could compete, in the estimation of its advocates, with Christianity, as neo-Pythagoreanism did, by setting up the claim that in the teachings of its founder it had a "way of life" preferable to that taught by the Founder of Christianity. |
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http://www.newadvent.org/cathen/12587b.htm
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| | Pythagoras |
| | Through them a divine order was imposed on the world, invisible to the eye but discernible by the mind." | | | Pythagoras himself, apparently escaped and later was murdered by his opposers." | | | (Indeed, Pythagoras was also said to have adopted the idea, current in Scythia and Thrace under the title of Orphism, of a process of bilocation, according to which the soul could be temporarily detached from the body.) This redemptive purification would enable the soul to achieve harmony with the order and proportion of the universe. |
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http://www.mystae.com/restricted/streams/gnosis/pythagoras.html
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| | The Complete Pythagoras |
| | For the full text of The Complete Pythagoras, click here. | | | The Complete Pythagoras is a compilation of two books. | | | The second is entitled Pythagorean Library and is a complete collection of the surviving fragments from the Pythagoreans. |
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http://www.completepythagoras.net
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| | Geometry in Art & Architecture Unit 3 |
| | But the most direct statement comes from the renaissance architect Leone Battista Alberti (1404-1472), "[I am] convinced of the truth of Pythagoras' saying, that Nature is sure to act consistently. | | | Pythagoras and his followers died when their meetinghouse was torched. | | | Slide 3-2: Pythagoras in Raphael's School of Athens |
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http://www.dartmouth.edu/~matc/math5.geometry/unit3/unit3.html
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| | Philosophical Dictionary: Price-Pythagoras |
| | Divine Harmony: The Life and Teachings of Pythagoras | | | Apparently they also held with religious devotion that souls are naturally immortal and therefore transmigrate at death to other human or animal bodies. | | | Pythagoras Revived: Mathematics and Philosophy in Late Antiquity |
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http://www.philosophypages.com/dy/p9.htm
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| | Pythagoras Theorem |
| | Historical Note: while we call it Pythagoras' Theorem, it was also known by Indian, Greek, Chinese and Babylonian mathematicians well before he lived ! | | | Years ago, a man named Pythagoras found an amazing fact about triangles: | | | If we know the lengths of two sides of a right angled triangle, then Pythagoras' Theorem allows us to find the length of the third side. |
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http://www.mathsisfun.com/pythagoras.html
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| | Editor's Introduction to the 1995 Hypertext Edition of Fitz Hugh Ludlow's The Hasheesh Eater |
| | It contains no mention of travel in the Near East, nor any references to the events in the September article except to say that the author had read the article and found it to be very similar to his own experiences ("The recital given there seemed written out of my own soul."). | | | The first, appearing in April of 1854 and entitled "The Vision of Hasheesh," is Bayard Taylor's story (although more than one source has wrongly attributed it to Ludlow) which would be incorporated into Taylor's 1855 book | | | The third article was published three months later and is entitled "The Apocalypse of Hasheesh." Also published anonymously, it is clearly Ludlow's work, containing his hallmark speculations on hashish use by Pythagoras, for instance. |
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http://users.lycaeum.org/~sputnik/Ludlow/THE/Introduction
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| | Pythagoras |
| | This theorem was probably known to the Babylonians a thousand years before Pythagoras, but he (or one of his disciples) was probably the first to prove it. | | | Pythagoras founded a school where he and his followers were responsible for developments in mathematics, astronomy, and music. | | | Pythagoras, the man for whom this theorem was names, was born about 580 B.C. and died around 500 B.C. He lived on the island of Samos in the Aegean Sea, Egypt, Babylon, and southern Italy. |
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http://www.coe.tamu.edu/~strader/Mathematics/Algebra/Pythagoras
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| | The Prime Glossary: Pythagoras |
| | A central belief of Pythagoras and his followers was that "everything is number." To the Pythagoreans a number was a quantity that could be expressed as a ratio of two integers (a rational number). | | | The Pythagoreans vowed to keep this discovery a secret, but the secret was later revealed by one of the members. | | | Pythagoras (circa 580 - 500 B.C.) was a native of the Aegean Island of Samos and founded a school in southern Italy. |
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http://primes.utm.edu/glossary/page.php?sort=Pythagoras
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| | Pythagoras |
| | Demonstration of Pythagoras’ theory for 3, 4, 5 triangle. | | | There have been many proofs of Pythagoras’ Theorem (there are 38 at http://www.cut-the-knot.org/pythagoras/) but one of the clearest and easiest to understand is the one used by Pythagoras himself. | | | Pythagoras himself is best known for proving that the Pythagorean Theorem was true. |
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http://www.nzmaths.co.nz/Measurement/Length/Pythagoras.htm
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| | MathsNet: Interactive Pythagoras's Theorem |
| | Pythagoras argued that there are three kinds of men. | | | About 530 BC Pythagoras settled in Crotona, a Greek colony in southern Italy, where he founded a movement with religious, political, and philosophical aims, known as Pythagoreanism. | | | Pythagoras is said to have been driven from Sámos by his disgust for the tyranny of Polycrates. |
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http://www.mathsnet.net/dynamic/pythagoras
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| | Pythagoras of Samos |
| | Because no reliable contemporary records survive, and because the school practiced both secrecy and communalism, the contributions of Pythagoras himself and those of his followers cannot be distinguished. | | | Pythagoras of Samos, c.560-c.480 BC, was a Greek philosopher and religious leader who was responsible for important developments in the history of mathematics, astronomy, and the theory of music. | | | Pythagoreans believed that all relations could be reduced to number relations ("all things are numbers"). |
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http://euler.ciens.ucv.ve/English/mathematics/pitagora.html
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| | Pythagoras summary |
| | The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it. | | | Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. |
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http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html
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| | Musical Theory |
| | It demonstrates how every element of Pythagorean tuning theory was implicit in the mathematics and mythology of that land for at least a thousand years, and perhaps two thousand, before Greek rationalists finally abstracted what we are willing to recognize as science from its long incubation within mythology. | | | It awoke to number theory only when it became acquainted with Mesopotamian methods. | | | Notice that Ea/Enki, god 40, defines these frames (DA falling and G:D rising) in his double role as 40:60 and 60:40 and thus literally "organizes the earth" (as represented by the string) into do, fa, sol, do, harmonic foundations of the modern scale. |
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http://www.new-universe.com/pythagoras/mcclain.html
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| | NOVA Online The Proof Pythagoras |
| | Although the theorem is named for Pythagoras, there is evidence that it may have been known by earlier civilizations. | | | They then generalized this rule for 3-4-5 triangles to apply to all right triangles. |
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http://www.pbs.org/wgbh/nova/proof/puzzle/pythagoras.html
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| | Pythagoras - Architecture and Music - general principles |
| | Pythagoras is said to have taken refuge in Metapontum where he died. | | | He was the son of a grain merchant who been granted Samoan citizenship for bringing grain to the city at a time of famine. | | | But the system of thought represented by a Pythagorean tradition has been of great importance to discussions of harmony, during the middle ages via Boethius, and the renaissance and Baroque periods, and into the modern age. |
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http://www.philophony.com/sensprop/pythagor.html
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| | Pythagorean Theorem and its many proofs |
| | The statement of the Theorem was discovered on a Babylonian tablet circa 1900-1600 B.C. Whether Pythagoras (c.560-c.480 B.C.) or someone else from his School was the first to discover its proof can't be claimed with any degree of credibility. | | | This proof is due to Douglas Rogers who came upon it in the course of his investigation into the history of Chinese mathematics. | | | Pythagoras' Theorem, by Bill Casselman, The University of British Columbia. |
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http://www.cut-the-knot.org/pythagoras/index.shtml
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| | The School of Pythagoras |
| | This site is dedicated to the mysteries of number and proportion. | | | Contemporary developments in sacred geometry, cosmology, music, sound and acoustics along with new interpretations of ancient architecture are some of the other areas of focus. | | | The work of Pythagoras provides a starting point for ongoing explorations of these topics. |
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http://www.new-universe.com/pythagoras
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| | Quotes by Pythagoras |
| | They are as follows: Ne'er suffer sleep thine eyes to close Before thy mind hath run O'er every act, and thought, and word, From dawn to set of sun; For wrong take shame, but grateful feel If just thy course hath been; Such effort day by day renewed Will ward thy soul from sin. | | | 6 Golden Verses So-called because they are "good as gold." They are by some attributed to Epicarmos, and by others to Empedocles, but always go under the name of Pythagoras, and seem quite in accordance with the excellent precepts of that philosopher. |
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http://www.zaadz.com/quotes/authors/pythagoras
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| | AMESA publications |
| | Learning and Teaching Mathematics aims to provide a medium for stimulating and challenging ideas, offering innovation and practice in all aspects of mathematics teaching and learning. | | | Click here for some recent articles from Pythagoras. | | | It seeks to reflect the variety of research concerns, the range of research methods employed and the variety of didactical, methodological and pedagogical issues in the teaching of Mathematics. |
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http://academic.sun.ac.za/mathed/AMESA/Publications.htm
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