Roman copy of a Greek bust Introduction Pythagoras of Samos c. He was the founder of the influential philosophical and religious movement or cult called Pythagoreanismand he was probably the first man to actually call himself a philosopher or lover of wisdom. Pythagoras or in a broader sense the Pythagoreansallegedly exercised an important influence on the work of Plato.
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.
It is a great tribute to the Pythagoreans' intellectual achievements that they deduced the special place of the number 10 from an abstract mathematical argument rather than from something as mundane as counting the fingers on two hands.
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: One of the simplest proofs comes from ancient Chinaand probably dates from well before Pythagoras' birth.
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.
This discovery rather shattered the elegant mathematical world built up by Pythagoras and his followers, and the existence of a number that could not be expressed as the ratio of two of God's creations which is how they thought of the integers jeopardized the cult's entire belief system.
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:Pythagoras is born in AD he is greek he make triangle problems for maths to make maths more boring.
There are few women that have made an impact on the math society compared with the number of men. A person can ramble off names such as Isaac Newton, Albert Einstein, Pythagoras of Samos, and Jean-François Niceron.
Pythagoras and His Contributions to Modern Society By Alex Who Was Pythagoras? Pythagoras was born C.
B.C. on an island named Samos in the Aegean Sea. He . Pythagoras also invented a lot of number patterns. Plato and Aristotle were influenced by Pythagoras's way of thinking. Also, he was a Greek religious leader who made huge developments in math that may have changed the math world.
Pythagoras was born in Samos and traveled widely in search of wisdom. He settled in Crotona, a Greek colony in Italy, about BC, and soon attracted disciples who devoted themselves to the study of cosmology, science, and philosophy.
Transcript of Pythagoras and His Contributions to Modern Society. Pythagoras and His Contributions to Modern Society By Alex Who Was Pythagoras? Pythagoras' pioneering ideas influenced many future astronomers, such as Copernicus, and had a large impact on NASA and space travel scientists.
Pythagoras' knowledge of the cosmos was made .