Did Pythagoras visit india? Who else among ancient Greek scholars visited India to learn?
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Pythagoras, the famous mathematician and contemporary of Socrates among the Greek philosophers belonged to the 6th century B.C.(569 - 475 B.C.) Apastamba Sulba Sutra, a set of mathematical formulas and principles belonged to 8th century B.C. and was in use in India which contains a list of Pythagorian Triples. It is indicative of the fact that Pythagoras learnt it from India before teaching the Greeks. Accoding to Albert Burk, Pythagoras copied it on his visit to India. Lecky in his 'History of European Morals' quotes an old tradition in Greece that Pythagoras had learnt in India from gymnosophists.\n\nPythagoras was a vegetarian and believed in transformation of human soul. He believed and lived like Indians that only by purifying your body you can attain divine powers and at the end merge with divinity. Hence, he insisted that a disciple should first be formally initiated by a preceptor who himself must be pure so that he can impart knowledge to others. Hindu thought also exerted a great influence on ancient Greek thought as M.E. Pococke shows in his 'India in Greece'.It is believed that besides Pythagoras, Appolonius, Democritus, Anaxarchus and Pyrrho also visited India. According to Lucianus, the Golden Philosophy first descended upon "the Indians, the mightiest nation upon the earth".\n\nThe famous Pythagorean Theorem was not in use for five hundred years after death of Pythagoras. It was Cicero and Plutarch who attributed the theorem to Pythagoras, though according to Sir Thomas L. Heath, there is no attribution by Pythagoras himself during his lifetime.
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Well, ancient India developed writing (Sanskrit) before almost everyone (with the exception of the Cuniform found in Mesopotamia).  Additionally, in India they developed cities, a complex caste system (where people were divided into different socioeconomic classes) and a strong written and oral tradition (see the Vedas, the Baghavadgita, etc).  Additionally, there are many who believe that India had the first real civilization as much as 14000 years ago, but that their initial advancement was set back by a rise in the sealevel due to glacial runoff (the thawing of the most recent ice age, actually).  There are even speculations that they possessed advance techology.  For example, there is an account in the Gita about a weapon that sounds a lot like a nuclear weapon.  Additionally, Alexander the Great (not a guy known for exageration) swore up and down that when he invaded that area he was attacked by "flying machines".  Very interesting story.
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my advice is to look for a history book, but also you can check wikipedia:\n\nGreek mathematics studied before the Hellenistic period refers only to the mathematics of Greece. Greek mathematics studied from the time of the Hellenistic period (from 323 BC) refers to all mathematics of those who wrote in the Greek language, since Greek mathematics was now not only written by Greeks but also non-Greek scholars throughout the Hellenistic world, which was spread across the Eastern end of the Mediterranean. Greek mathematics from this point merged with Egyptian and Babylonian mathematics to give rise to Hellenistic mathematics. Most mathematical texts written in Greek were found in Greece, Egypt, Mesopotamia, Asia Minor, Sicily and Southern Italy.\n\nAlthough the earliest found Greek texts on mathematics were written after the Hellenistic period, many of these are considered to be copies of works written during and before the Hellenistic period. Nevertheless, the dates of Greek mathematics are more certain than the dates of earlier mathematical writing, since a large number of chronologies exist that, overlapping, record events year by year up to the present day. Even so, many dates are uncertain; but the doubt is a matter of decades rather than centuries.\n\nGreek mathematics is thought to have begun with Thales (c. 624—c.546 BC) and Pythagoras (c. 582—c. 507 BC). Although the extent of the influence is disputed, they were probably influenced by the ideas of Egypt, Mesopotamia and less likely[citation needed], India. Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. According to Proclus' commentary on Euclid, Pythagoras stated the Pythagorean theorem and constructed Pythagorean triples algebraically. It is generally conceded that Greek mathematics differed from that of its neighbors in its insistence on axiomatic proofs.[8]\n\nGreek and Hellenistic mathematicians were the first to give a proof for irrational numbers (due to the Pythagoreans), and the first to develop Eudoxus's method of exhaustion, and the Sieve of Eratosthenes for uncovering prime numbers. They took the ad hoc methods of constructing a circle or an ellipse and developed a comprehensive theory of conics; they took many various formulas for areas and volumes and deduced methods to separate the correct from the incorrect and generate general formulas. The first recorded abstract proofs are in Greek, and all extant studies of logic proceed from the methods set down by Aristotle. Euclid, in the Elements, wrote a book that would be used as a mathematics textbook throughout Europe, the Near East and North Africa for almost two thousand years. In addition to the familiar theorems of geometry, such as the Pythagorean theorem, The Elements includes a proof that the square root of two is irrational and that there are infinitely many prime numbers.\n\nSome say the greatest of Greek mathematicians, if not of all time, was Archimedes (287—212 BC) of Syracuse. According to Plutarch, at the age of 75, while drawing mathematical formulas in the dust, he was run through with a spear by a Roman soldier. Roman society has left little evidence of an interest in pure mathematics.\n\n\nEuropean Renaissance mathematics (c. 1200—1600)\n\nIn Europe at the dawn of the Renaissance, most of what is now called school mathematics -- addition, subtraction, multiplication, division, and geometry -- was known to educated people, though the notation was cumbersome: Roman numerals and words were used, but no symbols: no plus sign, no equal sign, and no use of x as an unknown. Most of the mathematics now taught at universities was either known only to the mathematical community in India or had yet to be investigated and developed in Europe.\n\nThrough Latin translations of Arabic texts, knowledge of the Hindu-Arabic numerals and other important developments of Islamic and Indian mathematics were brought to Europ
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At the Harappa & Mohinjidharo excavations, believed to be primary Indian Cities, many seals belonging to Mesopotamia & Greek are found making them the first foriegn traders to trade with India.
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Euclid of Alexandria, the ancient Greek mathematician and author of the Elements \n\nclick here:http://en.wikipedia.org/wiki/Euclid\nhttp://en.wikipedia.org/wiki/Euclid%27s_Elements
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Aristotle\n\n\n: Αριστοτέλης, Aristotélēs) (384 BC – March 7, 322 BC) was an ancient Greek philosopher, a student of Plato and teacher of Alexander the Great. He wrote books on many subjects, including physics, poetry, zoology, logic, rhetoric, government, and biology. Aristotle, along with Plato and Socrates, is generally considered one of the most influential of ancient Greek philosophers. They transformed Presocratic Greek philosophy into the foundations of Western philosophy as we know it. The writings of Plato and Aristotle founded two of the most important schools of Ancient philosophy.\n\nhttp://www.ancientlibrary.com/medicine/0051.html
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ARYABHATA [Aryabhata] , c.476-550, Hindu mathematician and astronomer. He is one of the first known to have used algebra; his writings include rules of arithmetic and of plane and spherical trigonometry, and solutions of quadratic equationsr.
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Pythagoras (of Samos, born about 569-82 BC - died about 507 BC) was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. 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. \n\nIn any right triangle, the area of the square whose side is the hypotenuse (the long side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse, the adjacent and opposite in sine, cosine and tangent workings). \n\nIf we let c be the length of the hypotenuse and a and b be the lengths of the other two sides, the theorem can be expressed as the equation\n\nThis equation provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found.\n\nI was taught this in a long jumpo sand pit, with 25 billard balls.\nmy old teacher, Mr Chadwick, made a line of 5 balls, and this was the hypotenuse. he then drew in the rest of the triangle. he squared the 5 balls, by making a square of 5 by 5 balls, (25 in all).\n\nthen he put balls on the other lines. three fitted onto the short side, and four onto the next side. he then squared the two other sides. 3 x3 and 4 x 4 (9 and 16, when added together = 25. \n\nhe showed me that 27 years ago, It was amazing, and the reason I am now a teacher.
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I would google the name Aristarchus.\nIf nothing comes up, try adding greek mathematician.
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The ancient Greeks believed Atlas, the giant who supported the Heavens, lived beyond the Columns of Hercules (today's Gibraltar). Thus the ocean beyond those columns came to be known as the Ocean of Atlas, or Atlantic.\n\nThe East Indies were a source of spices and precious materials for Europe and the Middle East since the IXth century. The people living in that area (modern Indonesia, India and Pakistan) were called "Indian" because they were native (indigenous) to that region. The ocean is named after them.\n\nThe Pacific was 'discovered' by Spanish explorer Vasco Núñez de Balboa around 1500. He noticed how calm the waters near the shore of Panama were, and wrongfully assumed the whole sea in front was just as calm. He called it Pacific.
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Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a main inspirational source for Plato and platonism.\n\nLater resurgence of ideas similiar to those held by the early Pythagoreans are collected under the term neopythagoreanism.\n\nPythagorean thought was dominated by mathematics, but it was also profoundly mystical. In the area of cosmology there is less agreement about what Pythagoras himself actually taught, but most scholars believe that the Pythagorean idea of the transmigration of the soul is too central to have been added by a later follower of Pythagoras. On the other hand it is impossible to determine the origin of the Pythagorean account of substance. It seems that the Pythagorean account begins with Anaximander's account of the ultimate substance of things as "the boundless," by Anaximander called the "apeiron." On the other hand, the Pythagorean account says that it is through the notion of the "limit" that the "boundless" takes form.\n\nPythagoras wrote nothing down, and relying on the writings of Parmenides, Empedocles, Philolaus and Plato (people either considered Pythagoreans, or whose works are thought deeply indebted to Pythagoreanism) results in a very diverse picture in which it is difficult to ascertain what the common unifying Pythagorean themes were. Relying on Philolaus, whom all scholars agree should be highly representative of the Pythagorean school, one has a very intricate picture. Aristotle explains how the Pythagoreans (by which he meant the circle around Philolaus) developed Anaximander's ideas about the apeiron and the peiron, the unlimited and limited, by writing that:\n\n"… for they [the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit."\n\nContinuing with:\n\n"The Pythagoreans, too, held that void exists, and that it enters the heaven from the unlimited breath – it, so to speak, breathes in void. The void distinguishes the natures of things, since it is the thing that separates and distinguishes the successive terms in a series. This happens in the first case of numbers; for the void distinguishes their nature."\n\nWhen the apeiron is inhaled by the perion it causes separation, which also apparently means that it "separates and distinguishes the successive terms in a series." Instead of an undiffrentiated whole we have a living whole of inter-connected parts separated by "void" between them. This inhalation of the apeiron is also what makes the world mathematical, not just possible to describe using math, but truly mathematical since it shows numbers and reality to be upheld by the same principle: both the continuum of numbers (that is yet a series of successive terms, separated by void) and the field of reality, the cosmos - both are a play of emptiness and form, apeiron and peiron. What really sets this apart from Anaximander's original ideas is that this play of apeiron and peiron must take place according to harmonia (harmony), about which Stobaeus commentated:\n\n"About nature and harmony this is the position. The being of the objects, being eternal, and nature itself admit of divine, not human, knowledge – except that it was not possible for any of the things that exist and are known by us to have come into being, without there existing the being of those things from which the universe was composed, the limited and the unlimited. And since these principles existed being neither alike nor of the same kind, it would have been impossible for them to be ordered into a universe if harmony had not supervened – in whatever manner this came into being. Things that were
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The earliest known mathematics in ancient India dates back to circa 3000 BC during the Indus Valley Civilization. After its collapse in 1700 BC however, writing was absent in South Asia for a long period. There is considerable controversy regarding the dates when writing was re-developed in India and when the Brahmi script was developed.[10] Some scholars, such as Georg Bühler, date the Brahmi script as early as the 8th century BC, others from the Maurya dynasty in the 4th century BC. Recent archeological evidence dates it to 600 BC (see Brāhmī), while some scholars even suggest 1000 BC.[11] If the earlier dates are correct, it is possible that Pythagoras traveled to India and learnt mathematics there, as some have claimed (such as Florian Cajori). If the later date is correct, then Indian mathematics may have benefited from contact with Greece following the invasion of Alexander. It is also likely that the two mathematical traditions developed independently.\n\nAfter the Iron Age began, the progress of Indian mathematics has been fairly continuous until the 16th century AD, but it can be divided into roughly two periods of development. This section summarizes the period between 800 BC and 200 BC, when Indian mathematics wasn't studied for the sole purpose of science, but there are still advanced mathematics scattered throughout a large body of Indian texts from this period. Many of these however, are of uncertain date and authorship, and did not follow a serious mathematical tradition.\n\nThe Yajur-Veda composed by 900 BC, first explained the concept of numeric infinity. Yajnavalkya (circa 900-800 BC) computed the value of π to 2 decimal places. The Sulba Sutras (circa 800-600 BC) were geometry texts that first used irrational numbers, prime numbers, the rule of three, cube roots, computed the square root of 2 to five decimal places, gave the method of squaring the circle, solved linear equations and quadratic equations, discovered Pythagorean triples algebraically, and gave a numerical proof of the Pythagorean theorem.\n\nThe linguist Panini formulated the grammar rules for Sanskrit in the 5th century BC. His notation was similar to modern mathematical notation, and used metarules, transformations, and recursions with such sophistication that his grammar had the computing power equivalent to a Turing machine. Panini's work is also the forerunner to modern formal language theory (precursor to computing), while the Panini-Backus form used by most modern programming languages is also significantly similar to Panini's grammar rules. Pingala (4th-3rd century BC) invented the binary number system, Fibonacci series and Pascal's triangle, and also used a dot to denote zero and described the formation of a matrix. The works of Panini and Pingala were foundational to the development of computing.\n\nFrom 200 BC, mathematicians in India began studying mathematics for the sole purpose of science, starting with Jaina mathematicians between 200 BC and AD 200. They discovered transfinite numbers, set theory, logarithms, fundamental laws of indices, cubic equations, quartic equations, sequences and progressions, permutations and combinations, squaring and extracting square roots, and finite and infinite powers. Discoveries written in the Bakshali Manuscript include solutions of linear equations with upto five unknowns, the solution of the quadratic equation, arithmetic and geometric progressions, compound series, quadratic indeterminate equations, simultaneous equations, and the use of zero and negative numbers. Accurate computations for irrational numbers could be found, which includes computing square roots of numbers as large as a million to at least 11 decimal places.\n\nAryabhata in AD 499 introduced a number of trigonometric functions and trigonometric tables, techniques and algorithms of algebra, and obtained whole number solutions to linear equations by a method equivalent to the modern method, along with astrono
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Pythagoras{c.55o b.c.}
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the most fundamental contribution of ancient India in mathematics is the invention of decimal system of enumeration, including the invention of zero. The decimal system uses nine digits (1 to 9) and the symbol zero (for nothing) to denote all natural numbers by assigning a place value to the digits. The Arabs carried this system to Africa and Europe.The Vedas and Valmiki Ramayana used this system, though the exact dates of these works are not known. MohanjoDaro and Harappa excavations (which may be around 3000 B.C. old) also give specimens of writing in India. Aryans came 1000 years later, around 2000 B.C. Being very religious people, they were deeply interested in planetary positions to calculate auspicious times, and they developed astronomy and mathematics towards this end. They identified various nakshatras (constellations) and named the months after them. They could count up to 1012, while the Greeks could count up to 104 and Romans up to 108. Values of irrational numbers such as and were also known to them to a high degree of approximation. Pythagoras Theorem can be also traced to the Aryan's Sulbasutras. These Sutras, estimated to be between 800 B.C. and 500 B.C., cover a large number of geometric principles. Jaina religious works (dating from 500 B.C. to 100 B.C.) show they knew how to solve quadratic equations (though ancient Chinese and Babylonians also knew this prior to 2000 B.C.). Jainas used as the value of (circumference = x Diameter). They were very fond of large numbers, and they classified numbers as enumerable, unenumerable and infinite. The Jainas also worked out formulae for permutations and combinations though this knowledge may have existed in Vedic times. Sushruta Samhita (famous medicinal work, around 6th century B.C.) mentions that 63 combinations can be made out of 6 different rasas (tastes -bitter, sour, sweet, salty, astringent and hot).In the year 1881 A.D., at a village named Bakhshali near Peshawar, a farmer found a manuscript during excavation. About 70 leaves were found, and are now famous as the Bakhshali Manuscript. Western scholars estimate its date as about third or fourth century A.D. It is devoted mostly to arithmetic and algebra, with a few problems on geometry and mensuration.\nWith this historical background, we come to the famous Indian mathematicians.
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Aryabhatta - and other ancient Indian mathematicians.\n\nThe concept of zero, or Shunya was then taken by the Arabs to Europe.
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Euclid.\nGreek geometer who wrote the Elements , the world's most definitive text on geometry. The book synthesized earlier knowledge about geometry, and was used for centuries in western Europe as a geometry textbook. The text began with definitions, postulates ("Euclid's postulates "), and common opinions, then proceeded to obtain results by rigorous geometric proof. Euclid also proved what is generally known as Euclid's second theorem:  the number of primes  is infinite.  The beautiful proof Euclid gave of this theorem is still a gem and is generally acknowledged to be one of the "classic" proofs of all times in terms of its conciseness and clarity. In the Elements , Euclid used the method of exhaustion and reductio ad absurdum. He also discussed the so-called Euclidean algorithm  for finding the greatest common divisor  of two numbers, and is credited with the well-known proof of the Pythagorean theorem. \nNeither the year nor place of his birth have been established, nor the circumstances of his death, although he is known to have lived and worked in Alexandria for much of his life. In addition, no bust which can be verified to be his likeness is known (Tietze 1965, p. 8).
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Arabs learnt maths, Algebra and Zero from India. As well as other sciences. though they are known to be good in chemistry.\n\nIslamic astronomy and science was learnt from India. Arabs were good travellers and learnt things from all over the world.\n\n## Thats why they call numbers HINDSA (from India=Hind)\n\nJaipur was built by Hindu kings.\n\nTaj Mahal is controversial . Many say it was originally a Shiva temple.\n\nMuslim destroyed Buddhists!\n\nDo you know From Bukhara to Afghanistan and up to Bihar Islam  Went with a sword?\n\nDo you know About Hindu genocide by Muslims ? which has been going on for 1200 years?\n\nDo you know that HINDUKUSH means Hindu + kush(slaughter)\n\nSo many Hindu slaves died in few days at the hand of Muslims that that place is still known after the victims.\n\nMuslims burned down Universities of Takshshila and Nalanda which were renowned internationally? \n\nThe library was so vast that even after six month it was burning and some travellers claimed that even after 3 years some smoke could be seen ??\n\nThe Muslims who came to India were illiterate soldiers and invaders not architects.\n\nThe buildings are very much art of Hindu artists.Most of the buildings were made using debris and structures of Hindu temples.\n\nMore than 3000 Hindu temples were destroyed by Muslims.\n\nAldous Huxley :  \n\n"Islam's black record of holy wars and persecution - a record comparable to that of later Christianity."\n\nHe mention in his book, Ends and Means, "It is an extremely significant fact that, before the coming of the Mohammedans, there was virtually no persecution in India. The Chinese pilgrim Hiuen Tsang, who visited India in the first half of the seventh century and has left a circumstantial account of his 14 years in the country, makes it clear that Hindus and Buddhist lived side by side without any show of violence. Neither Hinduism or Buddhism is disgraced by anything corresponding to the Inquisition; neither was ever guilty of such iniquities as the Albigensian crusade or such criminal lunacies as the religious wars of the 16th and 17the centuries." \n\nFrancois Gautier, a political analyst for Le Figaro, one of France's largest circulation newspaper. In his book - Rewriting Indian History he observes: \n\n"Let it be said right away: the massacres perpetrated by Muslims in India are unparalleled in history, bigger than the holocaust of the Jews by the Nazis; or the massacre of the Armenians by the Turks; more extensive even than the slaughter of the South American native populations by the invading Spanish and Portuguese." \n\n“India has been a wounded civilization because of Islamic violence: Pakistanis know this; indeed they revel in it. ... We should face facts: Islamic rule in India was at least as catastrophic as the later Christian rule. The Christians created massive poverty in what was a most prosperous country; the Muslims created a terrorized civilization out of what was the most creative culture that ever existed.”\n\n(source: OutlookIndia.com, 15 November 1999 and  http://www.indpride.com/vsnaipaul.html).