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Pythagoras and his contributions
Pythagoras contribution to mathematics
Pythagoras contribution to mathematics
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Pythagoras was born approximately 570 B.C. on Samos, an island located near the western coast of Asia Minor. It is said that mathematicians such as Thales and Anaximander had tutored him. Thales had influenced him to pursue his education in Egypt. In 525 BC, when Cambyses II conquered Egypt, Pythagoras was held captive in Babylon where he became associated with the Magi priesthood; under their teachings, he grew more knowledgeable in mathematics, geometry, and music.
Pythagoras founded the Pythagorean School of Mathematics in Cortona and the semicircle.
Around 518 BC, in southern Italy, Pythagoras was the head of a mathematical society with an inner circle of followers known as mathematikoi. Pythagoras’s followers lived permanently with the Society, had no personal possessions and were vegetarians. The beliefs that Pythagoras held were that at its deepest level, reality is mathematical in nature, that philosophy can be used for spiritual purification,that the soul can rise to union with the divine, that certain symbols have a mystical significance, and that all brothers of the order should observe strict loyalty and secrecy.
Although we have some idea of what Pythagoras studied (properties of numbers that are similar to modern mathematics, such as even and odd numbers, triangular numbers, perfect numbers) his teachings within the schools and the society were very secretive and mysterious. There is little information pertaining to his process of creating famous mathematical formulas such as the Pythagorean Theorem (a2 + b2 = c2).
Among the many other mysteries surrounding Pythagoras, the cause of his death remains one of the most famous. There are two theories 1) There was an uprising against the Pythagoreans that ...
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...in mathematics / Marcus du Sautoy. Includes bibliographical references (p. [317]-322) and index. New York : HarperCollins, c2003. http://people.maths.ox.ac.uk/dusautoy/
The music of Pythagoras : how an ancient brotherhood cracked the code of the universe and lit the path from antiquity to outer space / Kitty Ferguson.
Includes bibliographical references (p. [347]-353) and index.
New York : Walker, 2008. http://kitty-ferguson.com/books Pythagoras : pioneering mathematician and musical theorist of Ancient Greece / Dimitra Karamanides. New York : Rosen Pub. Group, c2006.
Pythagoras and Music. Melanie Richards, M.Mus., S.R.C. Rosicrucian Digest No. 12009 https://www.rosicrucian.org/publications/digest/digest1_2009/05_web/07_richards/07_richards.pdf
The Pythagorean Theory of Music and Color. Fludd's De Musica Mundana.
http://www.sacred-texts.com/eso/sta/sta19.htm
... Brussard, Billee, ed., pp. 113- SummerMatters.com - "SummerMatters" 21 June. 2001. The 'Secondary' of the 'Secondary' Web.
Clarke, Leonard W.‘Greek Astronomy and Its Debt to the Babylonians' The British Journal for the History of Science, Vol. 1, No. (Cambridge University Press. 1962)
...rituals and traditions, they also developed their own in conjunction with the studies of mathematics, astronomy, music and metaphysics. The Pythagoreans also adopted and expanded upon the traditional secrecy policies of the mysteries. The central beliefs of the mystery cults were at the central beliefs of the Pythagoreans, but the Pythagoraeans developed and expanded (making minor changes to) the mystery cults using studies in education and philosophy.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
Nagle, Brendan D. (1979). The Ancient World: A Cultural and Social History. New Jersey: Prentice-Hall.
Burn, A. R.. Pericles and Athens. London: Hodder & Stoughton for the English Universities Press, 1948.
Archibald, Zofia. Discovering the World of the Ancient Greeks. New York: Facts On File, 1991. Print.
Robin Sowerby, The Greeks: An Introduction To Their Culture. Published in 1995 by Routledge Publishers.
Plato. "Gorgias.” Voices of Ancient Philosophy. Ed. Julia Annas. New York: Oxford, 2001. 305-318. Print.
The concept of impossible constructions in mathematics draws in a unique interest by Mathematicians wanting to find answers that none have found before them. For the Greeks, some impossible constructions weren’t actually proven at the time to be impossible, but merely so far unachieved. For them, there was excitement in the idea that they might be the first one to do so, excitement that lay in discovery. There are a few impossible constructions in Greek mathematics that will be examined in this chapter. They all share the same criteria for constructability: that they are to be made using solely a compass and straightedge, and were referred to as the three “classical problems of antiquity”. The requirements of using only a compass and straightedge were believed to have originated from Plato himself. 1
Thucydides. The History of the Peloponnesian War. Trans. David Grene. Chicago: University of Chicago, 1989. 115-18. Print.
The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
Euclid is one of the most influential and best read mathematician of all time. His prize work, Elements, was the textbook of elementary geometry and logic up to the early twentieth century. For his work in the field, he is known as the father of geometry and is considered one of the great Greek mathematicians. Very little is known about the life of Euclid. Both the dates and places of his birth and death are unknown. It is believed that he was educated at Plato's academy in Athens and stayed there until he was invited by Ptolemy I to teach at his newly founded university in Alexandria. There, Euclid founded the school of mathematics and remained there for the rest of his life. As a teacher, he was probably one of the mentors to Archimedes. Personally, all accounts of Euclid describe him as a kind, fair, patient man who quickly helped and praised the works of others. However, this did not stop him from engaging in sarcasm. One story relates that one of his students complained that he had no use for any of the mathematics he was learning. Euclid quickly called to his slave to give the boy a coin because "he must make gain out of what he learns." Another story relates that Ptolemy asked the mathematician if there was some easier way to learn geometry than by learning all the theorems. Euclid replied, "There is no royal road to geometry" and sent the king to study. Euclid's fame comes from his writings, especially his masterpiece Elements. This 13 volume work is a compilation of Greek mathematics and geometry. It is unknown how much if any of the work included in Elements is Euclid's original work; many of the theorems found can be traced to previous thinkers including Euxodus, Thales, Hippocrates and Pythagoras. However, the format of Elements belongs to him alone. Each volume lists a number of definitions and postulates followed by theorems, which are followed by proofs using those definitions and postulates. Every statement was proven, no matter how obvious. Euclid chose his postulates carefully, picking only the most basic and self-evident propositions as the basis of his work. Before, rival schools each had a different set of postulates, some of which were very questionable. This format helped standardize Greek mathematics. As for the subject matter, it ran the gamut of ancient thought. The
There are many people that contributed to the discovery of irrational numbers. Some of these people include Hippasus of Metapontum, Leonard Euler, Archimedes, and Phidias. Hippasus found the √2. Leonard Euler found the number e. Archimedes found Π. Phidias found the golden ratio. Hippasus found the first irrational number of √2. In the 5th century, he was trying to find the length of the sides of a pentagon. He successfully found the irrational number when he found the hypotenuse of an isosceles right triangle. He is thought to have found this magnificent finding at sea. However, his work is often discounted or not recognized because he was supposedly thrown overboard by fellow shipmates. His work contradicted the Pythagorean mathematics that was already in place. The fundamentals of the Pythagorean mathematics was that number and geometry were not able to be separated (Irrational Number, 2014).