Blog Pythagoras Pythagoras is a name most have us have heard of, but he is an enigma.
But, although his contribution was clearly important, he nevertheless remains a controversial figure. He left no mathematical writings himself, and much of what we know about Pythagorean thought comes to us from the writings of Philolaus and other later Pythagorean scholars.
Indeed, it is by no means clear whether many or indeed any of the theorems ascribed to him were in fact solved by Pythagoras personally or by his followers.
The school he established at Croton in southern Italy around BCE was the nucleus of a rather bizarre Pythagorean sect. Although Pythagorean thought was largely dominated by mathematics, it was also profoundly mystical, and Pythagoras imposed his quasi-religious philosophies, strict vegetarianism, communal living, secret rites and odd rules on all the members of his school including bizarre and apparently random edicts about never urinating towards the sun, never marrying a woman who wears gold jewellery, never passing an ass lying in the street, never eating or even touching black fava beans, etc.
The members were divided into the "mathematikoi" or "learners"who extended and developed the more mathematical and scientific work that Pythagoras himself began, and the "akousmatikoi" or "listeners"who focused on the more religious and ritualistic aspects of his teachings.
There was always a certain amount of friction between the two groups and eventually the sect became caught up in some fierce local fighting and ultimately dispersed. Resentment built up against the secrecy and exclusiveness of the Pythagoreans and, in BCE, all their meeting places were burned and destroyed, with at least 50 members killed in Croton alone.
Odd numbers were thought of as female and even numbers as male. The Pythagorean Tetractys The holiest number of all was "tetractys" or ten, a triangular number composed of the sum of one, two, three and four. However, Pythagoras and his school - as well as a handful of other mathematicians of ancient Greece - was largely responsible for introducing a more rigorous mathematics than what had gone before, building from first principles using axioms and logic.
Before Pythagoras, for example, geometry had been merely a collection of rules derived by empirical measurement. Pythagoras discovered that a complete system of mathematics could be constructed, where geometric elements corresponded with numbers, and where integers and their ratios were all that was necessary to establish an entire system of logic and truth.
Written as an equation: What Pythagoras and his followers did not realize is that this also works for any shape: It was Pythagoras, though, who gave the theorem its definitive form, although it is not clear whether Pythagoras himself definitively proved it or merely described it.
Either way, it has become one of the best-known of all mathematical theorems, and as many as different proofs now exist, some geometrical, some algebraic, some involving advanced differential equations, etc. Poor Hippasus was apparently drowned by the secretive Pythagoreans for broadcasting this important discovery to the outside world.
But the replacement of the idea of the divinity of the integers by the richer concept of the continuum, was an essential development in mathematics. It marked the real birth of Greek geometry, which deals with lines and planes and angles, all of which are continuous and not discrete.
The Pythagoreans also established the foundations of number theory, with their investigations of triangular, square and also perfect numbers numbers that are the sum of their divisors.
They discovered several new properties of square numbers, such as that the square of a number n is equal to the sum of the first n odd numbers e. They also discovered at least the first pair of amicable numbers, and amicable numbers are pairs of numbers for which the sum of the divisors of one number equals the other number, e.
Pythagoras is credited with the discovery of the ratios between harmonious musical tones Pythagoras is also credited with the discovery that the intervals between harmonious musical notes always have whole number ratios.
For instance, playing half a length of a guitar string gives the same note as the open string, but an octave higher; a third of a length gives a different but harmonious note; etc. Non-whole number ratios, on the other hand, tend to give dissonant sounds.
In this way, Pythagoras described the first four overtones which create the common intervals which have become the primary building blocks of musical harmony: The oldest way of tuning the note chromatic scale is known as Pythagorean tuning, and it is based on a stack of perfect fifths, each tuned in the ratio 3:The deaths of these rulers may have been a factor in Pythagoras's return to Samos but it is nowhere explained how Pythagoras obtained his freedom.
Darius of Persia had taken control of Samos after Polycrates' death and he would have controlled the island on Pythagoras's return. The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical. The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by Xenophanes of Colophon, who had been one of his contemporaries.
Pythagoreanism, philosophical school and religious brotherhood, believed to have been founded by Pythagoras of Samos, Almost all of the sources on Pythagoras' life and teachings date from long after his death, making the truth about him hard to discover.
Early life Born on the island of Samos, off Greece, in the Mediterranean Sea, Pythagoras was the son of Mnesarchus. Little is known about his early life. Pythagoras of Samos was a famous Greek mathematician and philosopher (c.
– c. BC). He is known best for the proof of the important Pythagorean theorem, which is about right triangles. He started a group of mathematicians, called the Pythagoreans, who worshiped numbers and lived like monks. He was an influence for Plato.
The deaths of these rulers may have been a factor in Pythagoras's return to Samos but it is nowhere explained how Pythagoras obtained his freedom. Darius of Persia had taken control of Samos after Polycrates' death and he would have controlled the island on Pythagoras's return.