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# PYTHAGORAS

Math class

by

Tweet## Meyrem Baer

on 17 May 2011#### Transcript of PYTHAGORAS

PYTHAGORAS Suite101.com,

What are Irrational Numbers?,

Public Domain

Image Credit http://www.suite101.com/view_image_articles.cfm/538537 Resume Birth Location: Island of Samos, Agean Sea

Date: 580 BC

Parents: Mother-Parthenis, Father- Mnesarshus Relations to the Island’s founders, who were considered gods. A merchant from Tyre, legend says he brought corn to Samos during a famine and was granted citizenship of Samos. Personal Information: The current basis for music theory, Pythagoras discovered that certain ratios equate pleasant harmonies. One day, Pythagoras was walking by a Blacksmith’s shop when he was stopped by the sounds of four different hammers pounding simultaneously. He realized, together, the sounds the hammers were producing a musical sound. After some experimentation, he realized the hammers weight ratios were six, eight, nine, and twelve. When he applied these ratios to a monochord, the same musical consonance was created by the chord as the hammers were producing. Upon further experimentation, he was able to name three musical ratios; they were: 2:1 (a musical octave), 3:2 (a musical fifth), and 4:3 (a musical fourth). During his time in Egypt, Pythagoras learned to apply a more mystical sense to numbers than what students learned in Greece. While Greece's Geometry was only in its infancy, the Egyptians were far advanced. Teaching Pythagoras to apply Math to very practical uses, he was a dedicated student. Egypt's educational centers were synonymous with the religious centers, and Pythagoras was educated in both realms. Several Egyptian characteristics are evident in Pythagoras' studies as the Egyptians related Math very closely to Religion, and the educated were very secretive of their knowledge and would not allow the masses to acquire it. After being exiled from Egypt due to the Persian King Cambyses taking rule of the country, Pythagoras spent 12 years studying with the Babylonian Magi, the city leaders who focused on religion and education. Here Pythagoras would have been educated in the application of arithmetic to predict planetary movement. These astrological movements were thought to be able to predict nature and human behavior. At the Ionian School, also known as Miletus, Pythagoras was the personal pupil of Thales, the founder of the school, and Anaximander, an ex-student of Thales. Under their direction, Pythagoras learned ideas which would influence him for the rest of his life. The ideas included everything from complex mathematical ideas all the way to avoiding meat. Part of the most influential aspect the two men had on Pythagoras was their suggestion for his to travel to Egypt. Pythagoras of Samos Complete Dictionary of Scientific Biography. Vol. 11. Detroit: Charles Scribner's Sons, 2008. p219-225

Pythagoras. The Liberart of Greek Philosophers. Karamanides, Dimitra.The Rosen Publishing Group. New York, NY. 2005

Pythagoras of Samos. O'Connor, J.J. and Robertson, E.F. School of St. Andrews, Scotland. http://www-history.mcs.st-andrews.ac.uk/Biographies/Pythagoras.html January 1999. Bibliography The first, and perhaps strongest, influence on Pythagoras was that of his first tutor, Pherecydes. As a boy, Pythagoras was a curious and intelligent person, who no doubt would have been inspired by Pherecydes, a well known member of the Temple of Apollo. Many of Pherecydes' ideas and opinions are evident as fundamentals to Pythagoras' own later beliefs. teaching of the “immortality of the soul” Thought and Math The contributions to Mathematics rests in numerology: the study of numbers influencing human life and affairs. Numbers were considered to be real, independent entities, as opposed to symbols or tools for counting. Believed to have personalities, Pythagoras attributed very specific characteristics to numbers.

It was believed that through math, could an understanding to the universe be found. Pythagoras used a very ancient form of writing numbers by using a series of dots to represent the numbers. This way, Pythagoras was able to see the physical change each number entailed. Triangular Numbers Square Numbers By seeing the transformation of numbers, Pythagoras applied his

observations to create groundbreaking discoveries. While historians have proven Pythagoras was not the inventor of the Pythagorean Theorem, he was the first to try and explain the science behind the theorem. Music and numbers are the central focus of the universe. music ratios. The current basis for music theory, Pythagoras discovered that certain ratios equate pleasant harmonies. Simply put, when a string in divided into certain ratios, the human brain recognizes the harmonies made to be pleasant. The ratios which Pythagoras has been accredited to finding are 2:1, 3:2, and 4:3. These ratios, including many others that have later been found are all used currently in the study of music theory. ἀκоυσματικоι (akousmatikoi)́, or “listeners” - were not allowed to speak, they memorized the master’s words, were not allowed to learn higherlevel mathematics

μαθηματικоί (mathematikoi), “scientist” or “mathematician.”- Those who had attained an advanced degree of knowledge after a long period of training. Were allowed to ask questions and express opinions of their own, lived by a very strict set of rules sum of the squares on the other two sides. the square on the hypotenuse is equal to the For a right angled triangle, Each planet had its own note as it orbited a focal point which was derived from musical ratios. The idea of a focal point nullified the then accepted idea of the Earth being the center of the universe. While the focal point deemed to be true by Pythagoras is incorrect, he was accredited by Copernicus for laying the groundwork for this own research on heliocentricity. Believed in a strict hierarchicy- divided his adherents into two groups: Meyrem Baer Pythagoras' followers attributed him to finding the sum of the angles in a rectangle as always being equal to two right angles.

Full transcriptWhat are Irrational Numbers?,

Public Domain

Image Credit http://www.suite101.com/view_image_articles.cfm/538537 Resume Birth Location: Island of Samos, Agean Sea

Date: 580 BC

Parents: Mother-Parthenis, Father- Mnesarshus Relations to the Island’s founders, who were considered gods. A merchant from Tyre, legend says he brought corn to Samos during a famine and was granted citizenship of Samos. Personal Information: The current basis for music theory, Pythagoras discovered that certain ratios equate pleasant harmonies. One day, Pythagoras was walking by a Blacksmith’s shop when he was stopped by the sounds of four different hammers pounding simultaneously. He realized, together, the sounds the hammers were producing a musical sound. After some experimentation, he realized the hammers weight ratios were six, eight, nine, and twelve. When he applied these ratios to a monochord, the same musical consonance was created by the chord as the hammers were producing. Upon further experimentation, he was able to name three musical ratios; they were: 2:1 (a musical octave), 3:2 (a musical fifth), and 4:3 (a musical fourth). During his time in Egypt, Pythagoras learned to apply a more mystical sense to numbers than what students learned in Greece. While Greece's Geometry was only in its infancy, the Egyptians were far advanced. Teaching Pythagoras to apply Math to very practical uses, he was a dedicated student. Egypt's educational centers were synonymous with the religious centers, and Pythagoras was educated in both realms. Several Egyptian characteristics are evident in Pythagoras' studies as the Egyptians related Math very closely to Religion, and the educated were very secretive of their knowledge and would not allow the masses to acquire it. After being exiled from Egypt due to the Persian King Cambyses taking rule of the country, Pythagoras spent 12 years studying with the Babylonian Magi, the city leaders who focused on religion and education. Here Pythagoras would have been educated in the application of arithmetic to predict planetary movement. These astrological movements were thought to be able to predict nature and human behavior. At the Ionian School, also known as Miletus, Pythagoras was the personal pupil of Thales, the founder of the school, and Anaximander, an ex-student of Thales. Under their direction, Pythagoras learned ideas which would influence him for the rest of his life. The ideas included everything from complex mathematical ideas all the way to avoiding meat. Part of the most influential aspect the two men had on Pythagoras was their suggestion for his to travel to Egypt. Pythagoras of Samos Complete Dictionary of Scientific Biography. Vol. 11. Detroit: Charles Scribner's Sons, 2008. p219-225

Pythagoras. The Liberart of Greek Philosophers. Karamanides, Dimitra.The Rosen Publishing Group. New York, NY. 2005

Pythagoras of Samos. O'Connor, J.J. and Robertson, E.F. School of St. Andrews, Scotland. http://www-history.mcs.st-andrews.ac.uk/Biographies/Pythagoras.html January 1999. Bibliography The first, and perhaps strongest, influence on Pythagoras was that of his first tutor, Pherecydes. As a boy, Pythagoras was a curious and intelligent person, who no doubt would have been inspired by Pherecydes, a well known member of the Temple of Apollo. Many of Pherecydes' ideas and opinions are evident as fundamentals to Pythagoras' own later beliefs. teaching of the “immortality of the soul” Thought and Math The contributions to Mathematics rests in numerology: the study of numbers influencing human life and affairs. Numbers were considered to be real, independent entities, as opposed to symbols or tools for counting. Believed to have personalities, Pythagoras attributed very specific characteristics to numbers.

It was believed that through math, could an understanding to the universe be found. Pythagoras used a very ancient form of writing numbers by using a series of dots to represent the numbers. This way, Pythagoras was able to see the physical change each number entailed. Triangular Numbers Square Numbers By seeing the transformation of numbers, Pythagoras applied his

observations to create groundbreaking discoveries. While historians have proven Pythagoras was not the inventor of the Pythagorean Theorem, he was the first to try and explain the science behind the theorem. Music and numbers are the central focus of the universe. music ratios. The current basis for music theory, Pythagoras discovered that certain ratios equate pleasant harmonies. Simply put, when a string in divided into certain ratios, the human brain recognizes the harmonies made to be pleasant. The ratios which Pythagoras has been accredited to finding are 2:1, 3:2, and 4:3. These ratios, including many others that have later been found are all used currently in the study of music theory. ἀκоυσματικоι (akousmatikoi)́, or “listeners” - were not allowed to speak, they memorized the master’s words, were not allowed to learn higherlevel mathematics

μαθηματικоί (mathematikoi), “scientist” or “mathematician.”- Those who had attained an advanced degree of knowledge after a long period of training. Were allowed to ask questions and express opinions of their own, lived by a very strict set of rules sum of the squares on the other two sides. the square on the hypotenuse is equal to the For a right angled triangle, Each planet had its own note as it orbited a focal point which was derived from musical ratios. The idea of a focal point nullified the then accepted idea of the Earth being the center of the universe. While the focal point deemed to be true by Pythagoras is incorrect, he was accredited by Copernicus for laying the groundwork for this own research on heliocentricity. Believed in a strict hierarchicy- divided his adherents into two groups: Meyrem Baer Pythagoras' followers attributed him to finding the sum of the angles in a rectangle as always being equal to two right angles.