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- 1. PYTHAGORAS OFSAMOSPythagoras was an influential Greek mathematicianand philosopher, best known for the theory to whichhe gave his name.
- 2. ●Pythagoras of Samos is often described as the first puremathematician. He is an extremely important figure in thedevelopment of mathematics yet we know relatively little about hismathematical achievements. Unlike many later Greekmathematicians, where at least we have some of the books whichthey wrote, we have nothing of Pythagorass writings. The societywhich he led, half religious and half scientific, followed a code ofsecrecy which certainly means that today Pythagoras is amysterious figure
- 3. EARLY LIFE●Born on the island of Samos, off Greece, in the MediterraneanSea, Pythagoras was the son of Mnesarchus. Little is knownabout his early life. After studying in Greece, he fled to southernItaly to escape the harsh rule of Polycrates (died c. 522 B.C.E. ),who came to power about 538 B.C.E. There he began teachingand soon had a clutch of students who lived a structured life ofstudy and exercise, inspired by a philosophy based aroundmathematics. This circle came to be known as the Pythagoreans.
- 4. EARLY LIFE●Pythagoras and his followers became politically powerful inCroton in southern Italy, where Pythagoras had established aschool for his newly formed sect, or group of followers. It isprobable that the Pythagoreans took positions in the localgovernment in order to lead men to the pure life that was directedby their teachings. Eventually, however, a rival group launched anattack on the Pythagoreans at a gathering of the sect, and thegroup was almost completely destroyed. Pythagoras either hadbeen forced to leave Croton or had left voluntarily shortly beforethis attack. He died in Metapontum early in the fifth century B.C.E.
- 5. PYTHAGOREANS●The early Pythagoreans were upper middle class and politicallyactive. They formed a moral elite who strove to perfect theirphysical form in this life in order to gain immortality in the next. Tofree the soul and achieve immortality, the mortal body had to berigorously disciplined to keep it morally pure and free of the basenature. Until this could be achieved the soul would be repeatedlyreincarnated, or transmigrated, until released by accumulatedmerit.
- 6. BELIEFS●Pythagoreans also believed in the cosmos, which at that timereferred to an idea of a clockwork order and beauty in the wholeuniverse. While probably believing in classical Greek polytheism,they maintained a superior divinity, the one, above all others.They had a number of taboos, including the avoidance of meatand beans, and lived by a series of rules governing all aspects oflife. In approximately 500 BC, there appears to have been anuprising against the power of the Pythagoreans. Pythagoras fledand is thought to have been killed or died shortly afterwards.
- 7. MATHEMATICAL TEACHINGS●So great was the Pythagoreans respect for the "Tetractys of theDecad" (the sum of 1 + 2 + 3 + 4) that they swore their oaths(promises) by it rather than by the gods, as was normal during hisday. Pythagoras may have discovered the theorem which stillbears his name (in right triangles [triangle with one angle equal to90 degrees], the square on the hypotenuse equals the sum of thesquares on the other sides), although this proposal has beendiscovered on a writing stone dating from the time of theBabylonian king Hammurabi (died c. 1750 B.C.E. ). Regardless oftheir sources, the Pythagoreans did important work in extendingthe body of mathematical knowledge.
- 8. MATHEMATICAL TEACHINGS●As a more general outline, the Pythagoreans presented the twocontraries (opposites), Limited and Unlimited, as ultimateprinciples, or truths. Numerical oddness and evenness areequated with Limited and Unlimited, as are one and plurality(many), right and left, male and female, motionlessness andmovement, straight and crooked, light and darkness, and goodand bad. It is not clear whether an ultimate One, or Monad, waspresented as the cause of the two categories.
- 9. PYTHAGORAS THEOREM ● His main discovery was the Pythagoras theorem: ●The theorem has numerous proofs, possibly the most of anymathematical theorem. ●These are very diverse, including both geometric proofs andalgebraic proofs, with some dating back thousands of years. ●The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects thatare not right triangles, and indeed, to objects that are not triangles at all,but n-dimensional solids. ●In any right-angled triangle, the square of the hypotenuse is equal tothe sum of the squares of the other two sides
- 10. DEATH●Pythagorass death is unknown. Some say he died in a revolt inwhich the meeting place of the Pythagoreans was surroundedand set to fire, of which only a few survived. Others say themembers formed a bridge using their bodies over the flames toallow Pythagoras to escape. He fled to Metapontum where hechose to die at the hands of his enemies rather than trample overa sacred bean field.

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