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# PYTHAGORAS

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by

Tweet## Christine B

on 29 October 2012#### Transcript of PYTHAGORAS

THE Man PYTHAGORAS IS he GREAT? The Eventful Man The Event-making Man GreatNESS Exploring 'Greatness' Is Pythagoras 'great'? Modern Historical Personal Different

perspectives 570 BCE adulthood early adulthood Conclusion Accomplishments Character Some Many Few potential Influence Life Concept BIRTH! Born in Samos, Ionia, Greece 490 BCE http://www.daphnet.org/ Traveled in search of knowlege.

Is said to have gone to Egypt. Rumoured to have a or multiple mentor(s) in academic pursuits. 530 BCE http://www.lib.utexas.edu/maps/historical/shepherd/italy_ancient_south.jpg Moved to and settled in Croton, Italy. Formed the 'Pythagorean Society'.

Became a leader. Had 1 son and 3 daughters. Died in Metapontum, Greece. Pythagoras himself was not and is not 'GREAT'. Accomplishments Philosophy Pythagorean Theorem Harmony of the Spheres Pythagorean Society Religion or way of life Irrational numbers Pythagorean Triples Fermat's last Theorem Properties of Numbers Character/

Historical outlook Myth and/or

Legend Fact Golden thigh Bit snakes to death Born wiser than man no written work produced no contemporaries No direct or solid evidence of:

philosophical beliefs

character Viewed as the

Hyperborean Apollo Divination and prophecy Impact Esoteric Groups/

Spirituality/

Philosophy People Recording of history (before modern times) Historical accuracy Fascination Accreditation Freemasonry Aristotelian Aristotle Archytas Modern Society Technological advancement The people of Pythagoras' time believed him to be a divine figure. Lawgiver Religious figure Hearing the voices of souls Most likely fed off of each other and created cycle of such information and belief. Traits: Charismatic

generous

wise

divine

pure Pythagoras wrote nothing, nor were there any detailed accounts of his thought written by contemporaries.

By the first centuries BCE, it became fashionable to present Pythagoras as a semi-divine figure, who originated all that was true in the Greek philosophical tradition, including many of Plato's and Aristotle's mature ideas. A number of treatises were forged in the name of Pythagoras and other Pythagoreans in order to support this view. Most, if not all Pythagoras accomplishments were likely attributed to Pythagoras by the Pythgoreans or myth, but not produced by him. Mathematics advancement Historic curiosity Pythgorean Society Plato Mathematical equations for musical notes Adherence to Pythagorean beliefs continued for over 100 years after his death. Career Education Philosopher

academic Students Mentor(s) Travel Cosmologist Mystic Mathematician Cosmologist Mystic Spiritual Leader His travel incluenced the historical accuracy of the chronology and origin of ideas. Gained knowledge from other civilizations and brought it back to Greek civilization for advancement. However, none are truly his. Cannot be proven that it was Pythagoras who influenced these outcomes. Overall, character is mythical. We find mentioned as his instructors:

Themistoclea

Creophylus

Hermodamas of Samos

Bias

Thales

Anaximander

Pherecydes of Syros

The Egyptians taught him geometry

Phoenicians taught arithmetic

the Chaldeans taught astronomy

the Magians taught the principles of religion and practical maxims for the conduct of life Though, it is not certain who his mentor/mentors were. Reputation Often described as first pure mathematician. Pythagoras was well educated.

He learned to:

play the lyre

recite Homer poetry Anaximander

interest in geometry and cosmology that influenced Pythagoras' own views It is not difficult to relate many of Pythagoras's beliefs, ones he would later impose on the society that he set up in Italy, to the customs that he came across in Egypt. For example the secrecy of the Egyptian priests, their refusal to eat beans, their refusal to wear even cloths made from animal skins, and their striving for purity were all customs that Pythagoras would later adopt. Porphyry says that Pythagoras learnt geometry from the Egyptians but it is likely that he was already acquainted with geometry, certainly after teachings from Thales and Anaximander. Porphyry writing 'Life of Pythagoras' commentary Ancient Society Politics in Samos Politics in Croton Melting pot Said to have been good friends with Polycrates and carried a letter of introduction to Egypt. Said to have viewed Polycrates' later rule as tyrannic. Pythagoreans opposed move to democracy. Although they had political sway, this led to their downfall. Beliefs and influences brought back from other cultures like Egypt shaped the Pythogorean way of life. Ultimately, gave a segue to the shift from strict religious belief. Iamblichus Syrian philosopher who played a large part in the development of Neoplatonism.

His writings which have survived include On the Pythagorean Life; The Exhortation to Philosophy; On the General Science of Mathematics; On the Arithmetic of Nicomachus; and Theological Principles of Arithmetic. Proclus He was a major influence on Proclus "Wherever there is number, there is beauty."

~ Proclus One of the last major Neoplatonist philosophers.

Great influence on Islamic and Western medieval thought. Neoplatonism Platonism Classical philosophy Founded on Plato's beliefs and theories.

Similar to the Pythagoreans because:

science and morals dogma

orphism beliefs

grouping of like minded thinkers

... he formed a school in the city [of Samos], the 'semicircle' of Pythagoras, which is known by that name even today, in which the Samians hold political meetings. They do this because they think one should discuss questions about goodness, justice and expediency in this place which was founded by the man who made all these subjects his business. Outside the city he made a cave the private site of his own philosophical teaching, spending most of the night and daytime there and doing research into the uses of mathematics... Pythagoras founded a philosophical and religious school (often seen as a brotherhood) in Croton that had many followers. Pythagoras was the head of the society with an inner circle of followers known as mathematikoi. The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules. 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 Both men and women were permitted to join. Pythagorean beliefs/rules

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

top physical form for soul immortality

refusal to ear beans

vegetarian

transmigration of souls The outer circle of the Society were known as the akousmatics and they lived in their own houses, only coming to the Society during the day. They were allowed their own possessions and were not required to be vegetarians. His first attempt: he founded a school called 'The Semicircle' in Samos. Iamblichus writes in the third century BCE that: Famous female philosophers http://www.mlahanas.de/Greeks/Bios/WomenPhilosopher.jpg Theano of Thurii (Pythagoras' wife)

Presumed work: 'Cosmology; Theorem of the golden mean, Theory of Numbers, Construction of the universe, On Virtue.' Damo of Crotona

daughter

Arignote of Samos

daughter

religious

Myia

daughter

poet and philosopher

Influenced a list of at least 17 Pythagorean females (referenced by Iamblichus) The Pythagorean's work Work was based on/driven by:

discovering principles of mathematics

concept of the number

concept of the triangle

concept of mathematical figures

abstract ideas and their proofs

Worked similar to the idea of a research group but also very different to the modern idea of research groups; their study was based on discovery and not so much problem solving.

It is hard for us today, familiar as we are with pure mathematical abstraction and with the mental act of generalisation, to appreciate the originality of this Pythagorean contribution.

~ Brumbaugh Their practice was also very secretive and communal. Thus, it was hard to distinguish between the work of Pythagoras and that of his followers. Discoveries also did not reach the public, but remained elite. Transforming geometry into liberal study After [Thales, etc.] Pythagoras transformed the study of geometry into a liberal education, examining the principles of the science from the beginning and probing the theorems in an immaterial and intellectual manner: he it was who discovered the theory of irrational and the construction of the cosmic figures.

~ Proclus Tetractys Essentially, many credit Pythagoras as the first pure mathematician because he transformed the concepts into pure abstract. Also, by forming a brotherhood, helped math flourish. The belief that all things have a mathematical root/are numbers stemmed from:

Pythagoras noticing that vibrating strings produce harmonious toes when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments. Again, there is some controversy as to HIS discovery of this; some say that he first referred to the ratio of the hammers that stuck the strings, and others refined the theory.

Either way, it formed a base for the Pythagorean's heaviest belief: The Pythagorean ... having been brought up in the study of mathematics, thought that things are numbers ... and that the whole cosmos is a scale and a number.

~ Aristole Music Great strides in musical theory and the mathematical theory of music were due to 'his' accomplishments. Pythagoras studied properties of numbers which would be familiar to mathematicians today, such as even and odd numbers, triangular numbers, perfect numbers, and etc.

However to Pythagoras numbers had personalities which we hardly recognize as mathematics today; masculine or feminine, perfect or incomplete, beautiful or ugly. This feeling modern mathematics has deliberately eliminated, but we still find overtones of it in fiction and poetry. Literature Overtones of number personalities. Ten was the very best number: it contained in itself the first four integers - one, two, three, and four [1 + 2 + 3 + 4 = 10] - and these written in dot notation formed a perfect triangle. http://www.american-buddha.com/pythagsource.1.gif Was used as a sacred symbol in Pythagorean society.

Tetractys also seen evident in Chinese, Kabbalists and etc, symbols. Likely coincidence. Cosmological belief that the planets moved in a musical (mathematically musical) harmony or rhythm. http://mathworld.wolfram.com/images/eps-gif/PythagoreanTheoremFigure_1000.gif http://www.grc.nasa.gov/WWW/k-12/airplane/Images/pythag.gif Legend has it that upon the completion of this theorem, Pythagoras sacrificed 100 oxen. http://www.geom.uiuc.edu/~demo5337/Group3/hist.html Euxdoxus:

200 years later found a way to deal with the 'unutterable' irrational numbers that the Pythagoreans discovered, but damned. More than 4000 years ago this concept was already known to the ancient Egyptians, Chinese, Indians and Babylonians. However, it is believed that Pythagoras was the first to prove it. http://ualr.edu/lasmoller/pythag.html Integers that satisfy the Pythagorean Theorem. http://www.geom.uiuc.edu/~demo5337/Group3/spiral.gif Euxdoxus Euclid Fermat http://www.math.utah.edu/~pa/math/flt.gif The sum of the angles of a triangle is equal to two right angles. Also, a polygon with n sides has sum of interior angles equal to 2n-4 right angles and sum exterior angles equal to four right angles. Solved equations by geometrical means The 5 regular solids. Taught that the Earth was a sphere at the center of the universe.

The orbit of the Moon was inclined to the equator of the Earth.

Realized that Venus was the same as an evening or morning star. http://jwilson.coe.uga.edu/EMAT6680/Parveen/golden16.gif Astronomy Greatly influenced religious belief that harmony ruled all; harmony of numbers, etc. And the inventions were so admirable, and so divinised by those who understood them, that the members used them as forms of oath: "By him who handed to our generation the tetractys, source of the roots of ever-flowing nature."

—Iamblichus, Vit. Pyth., 29 Much was due to the propaganda and zeal of the Pythagoreans. Part was also due to the lack of education of others. Therefore, Pythagoreans and Pythagoras was deemed elite and wise. Due to his semi-divine status, Pythagoras was often depicted as figure of authority or general admiration in art/paintings/murals Authority and mysticism come together making him rather influential. The influenced was mainly the Pythagoreans. It is said that he was often forced into political affairs due to his influence and wisdom. He chose to escape that for the most part. Was a sign of divinity.

Though this was untrue, it is likely that he had a large birthmark. To save a man, he bit snakes to death.

This was another semi-divine feat. It is said that his birth was prophesied and that he would be wiser than man. One writer, most likely trying to depict Pythagoras as a divine figure, told a story of:

Pythagoras walking in the city

he heard a puppy yelping

the puppy was being kicked by a man

he told the man to stop because the puppy was the reincarnation of the soul of his deceased friend Triangulation Trigonometry, whose fundamental principles are based on Pythagorean work, is used in triangulation technology and techniques.

ex: GSP Construction Easy integer construction of right angles and triangles are fundamental in construction for the triangle is the strongest shape.

An example of these uses is building struts and ties in roofs.

This basic and quick reference knowledge (such as the 3,4,5 triangle) is the basis of building and helped society focus on more complex problems. Shortest distance The converse Pythagorean theorem allows modern mathematicians or just people to find the shortest distance to a location.

This is also used the modern technologies like GPS. Engineering Oceanography

Meteorology

Geology

Aerospace

Electrical

Most if not everything electronic/electrical operates or was developed using the Pythagorean Theorem.

Engineering encompasses this because design these concepts.

Basically, any calculations using Trigonometry or logarithms used Pythagorean theorem. Having the fundamental principle: Pythagorean Theorem, allowed the development of fields like Trigonometry and Logarithms. This all allowed math to become more abstract. Physics Domain of abstract and practical applications of math and science.

Pythagoras was a segue to the development of abstract math or math as a liberal study. Metaphysics Domain of abstract and practical applications of math and science.

Pythagoras was a segue to the development of abstract math or math as a liberal study. Modern Society

as... More highly educated and technologically advanced society. Less religious and more scientific and spiritual. Platonism Rosicrucianism Aristotelian Classical philosophy Founded on Aristotle's beliefs and theories.

Idea of a group/brotherhood similar to the Pythagoreans; like minded thinkers grouped together. Claimed to have evolved from the Pythagoreans.

Opposed religious dogma.

Devoted to geometry/mathematics. Iamblichus Porphyry Diogenes Many historians are in conflict of just how influential Pythagoras was because of the lack of objective historical records. http://plato.stanford.edu/entries/pythagoras/ Both had strong agenda in favor of Pythagoras.

Claimed that all Greek Philosophers plagiarized from Pythagoras' ideas. Has written works on Pythagoras.

Had little objectivity. He was a student of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato. Not as great

no solid evidence of achievement

idea of person is influential Great

divine figure

enlightened

many accomplishments Not great

too much due to circumstance and perspective

The Pythagoreans as a group, due to THEIR accomplishments are considered greater Any man whose actions influenced by subsequent developments along quite a different course that would have been if followed if these actions had not been taken.

~ The Great Man Theory A man whose actions are the consequence of outstanding capacities of intelligence, will and character rather than of accidents of position.

~The Great Man Theory A perspective or bias.

Full transcriptperspectives 570 BCE adulthood early adulthood Conclusion Accomplishments Character Some Many Few potential Influence Life Concept BIRTH! Born in Samos, Ionia, Greece 490 BCE http://www.daphnet.org/ Traveled in search of knowlege.

Is said to have gone to Egypt. Rumoured to have a or multiple mentor(s) in academic pursuits. 530 BCE http://www.lib.utexas.edu/maps/historical/shepherd/italy_ancient_south.jpg Moved to and settled in Croton, Italy. Formed the 'Pythagorean Society'.

Became a leader. Had 1 son and 3 daughters. Died in Metapontum, Greece. Pythagoras himself was not and is not 'GREAT'. Accomplishments Philosophy Pythagorean Theorem Harmony of the Spheres Pythagorean Society Religion or way of life Irrational numbers Pythagorean Triples Fermat's last Theorem Properties of Numbers Character/

Historical outlook Myth and/or

Legend Fact Golden thigh Bit snakes to death Born wiser than man no written work produced no contemporaries No direct or solid evidence of:

philosophical beliefs

character Viewed as the

Hyperborean Apollo Divination and prophecy Impact Esoteric Groups/

Spirituality/

Philosophy People Recording of history (before modern times) Historical accuracy Fascination Accreditation Freemasonry Aristotelian Aristotle Archytas Modern Society Technological advancement The people of Pythagoras' time believed him to be a divine figure. Lawgiver Religious figure Hearing the voices of souls Most likely fed off of each other and created cycle of such information and belief. Traits: Charismatic

generous

wise

divine

pure Pythagoras wrote nothing, nor were there any detailed accounts of his thought written by contemporaries.

By the first centuries BCE, it became fashionable to present Pythagoras as a semi-divine figure, who originated all that was true in the Greek philosophical tradition, including many of Plato's and Aristotle's mature ideas. A number of treatises were forged in the name of Pythagoras and other Pythagoreans in order to support this view. Most, if not all Pythagoras accomplishments were likely attributed to Pythagoras by the Pythgoreans or myth, but not produced by him. Mathematics advancement Historic curiosity Pythgorean Society Plato Mathematical equations for musical notes Adherence to Pythagorean beliefs continued for over 100 years after his death. Career Education Philosopher

academic Students Mentor(s) Travel Cosmologist Mystic Mathematician Cosmologist Mystic Spiritual Leader His travel incluenced the historical accuracy of the chronology and origin of ideas. Gained knowledge from other civilizations and brought it back to Greek civilization for advancement. However, none are truly his. Cannot be proven that it was Pythagoras who influenced these outcomes. Overall, character is mythical. We find mentioned as his instructors:

Themistoclea

Creophylus

Hermodamas of Samos

Bias

Thales

Anaximander

Pherecydes of Syros

The Egyptians taught him geometry

Phoenicians taught arithmetic

the Chaldeans taught astronomy

the Magians taught the principles of religion and practical maxims for the conduct of life Though, it is not certain who his mentor/mentors were. Reputation Often described as first pure mathematician. Pythagoras was well educated.

He learned to:

play the lyre

recite Homer poetry Anaximander

interest in geometry and cosmology that influenced Pythagoras' own views It is not difficult to relate many of Pythagoras's beliefs, ones he would later impose on the society that he set up in Italy, to the customs that he came across in Egypt. For example the secrecy of the Egyptian priests, their refusal to eat beans, their refusal to wear even cloths made from animal skins, and their striving for purity were all customs that Pythagoras would later adopt. Porphyry says that Pythagoras learnt geometry from the Egyptians but it is likely that he was already acquainted with geometry, certainly after teachings from Thales and Anaximander. Porphyry writing 'Life of Pythagoras' commentary Ancient Society Politics in Samos Politics in Croton Melting pot Said to have been good friends with Polycrates and carried a letter of introduction to Egypt. Said to have viewed Polycrates' later rule as tyrannic. Pythagoreans opposed move to democracy. Although they had political sway, this led to their downfall. Beliefs and influences brought back from other cultures like Egypt shaped the Pythogorean way of life. Ultimately, gave a segue to the shift from strict religious belief. Iamblichus Syrian philosopher who played a large part in the development of Neoplatonism.

His writings which have survived include On the Pythagorean Life; The Exhortation to Philosophy; On the General Science of Mathematics; On the Arithmetic of Nicomachus; and Theological Principles of Arithmetic. Proclus He was a major influence on Proclus "Wherever there is number, there is beauty."

~ Proclus One of the last major Neoplatonist philosophers.

Great influence on Islamic and Western medieval thought. Neoplatonism Platonism Classical philosophy Founded on Plato's beliefs and theories.

Similar to the Pythagoreans because:

science and morals dogma

orphism beliefs

grouping of like minded thinkers

... he formed a school in the city [of Samos], the 'semicircle' of Pythagoras, which is known by that name even today, in which the Samians hold political meetings. They do this because they think one should discuss questions about goodness, justice and expediency in this place which was founded by the man who made all these subjects his business. Outside the city he made a cave the private site of his own philosophical teaching, spending most of the night and daytime there and doing research into the uses of mathematics... Pythagoras founded a philosophical and religious school (often seen as a brotherhood) in Croton that had many followers. Pythagoras was the head of the society with an inner circle of followers known as mathematikoi. The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules. 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 Both men and women were permitted to join. Pythagorean beliefs/rules

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

top physical form for soul immortality

refusal to ear beans

vegetarian

transmigration of souls The outer circle of the Society were known as the akousmatics and they lived in their own houses, only coming to the Society during the day. They were allowed their own possessions and were not required to be vegetarians. His first attempt: he founded a school called 'The Semicircle' in Samos. Iamblichus writes in the third century BCE that: Famous female philosophers http://www.mlahanas.de/Greeks/Bios/WomenPhilosopher.jpg Theano of Thurii (Pythagoras' wife)

Presumed work: 'Cosmology; Theorem of the golden mean, Theory of Numbers, Construction of the universe, On Virtue.' Damo of Crotona

daughter

Arignote of Samos

daughter

religious

Myia

daughter

poet and philosopher

Influenced a list of at least 17 Pythagorean females (referenced by Iamblichus) The Pythagorean's work Work was based on/driven by:

discovering principles of mathematics

concept of the number

concept of the triangle

concept of mathematical figures

abstract ideas and their proofs

Worked similar to the idea of a research group but also very different to the modern idea of research groups; their study was based on discovery and not so much problem solving.

It is hard for us today, familiar as we are with pure mathematical abstraction and with the mental act of generalisation, to appreciate the originality of this Pythagorean contribution.

~ Brumbaugh Their practice was also very secretive and communal. Thus, it was hard to distinguish between the work of Pythagoras and that of his followers. Discoveries also did not reach the public, but remained elite. Transforming geometry into liberal study After [Thales, etc.] Pythagoras transformed the study of geometry into a liberal education, examining the principles of the science from the beginning and probing the theorems in an immaterial and intellectual manner: he it was who discovered the theory of irrational and the construction of the cosmic figures.

~ Proclus Tetractys Essentially, many credit Pythagoras as the first pure mathematician because he transformed the concepts into pure abstract. Also, by forming a brotherhood, helped math flourish. The belief that all things have a mathematical root/are numbers stemmed from:

Pythagoras noticing that vibrating strings produce harmonious toes when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments. Again, there is some controversy as to HIS discovery of this; some say that he first referred to the ratio of the hammers that stuck the strings, and others refined the theory.

Either way, it formed a base for the Pythagorean's heaviest belief: The Pythagorean ... having been brought up in the study of mathematics, thought that things are numbers ... and that the whole cosmos is a scale and a number.

~ Aristole Music Great strides in musical theory and the mathematical theory of music were due to 'his' accomplishments. Pythagoras studied properties of numbers which would be familiar to mathematicians today, such as even and odd numbers, triangular numbers, perfect numbers, and etc.

However to Pythagoras numbers had personalities which we hardly recognize as mathematics today; masculine or feminine, perfect or incomplete, beautiful or ugly. This feeling modern mathematics has deliberately eliminated, but we still find overtones of it in fiction and poetry. Literature Overtones of number personalities. Ten was the very best number: it contained in itself the first four integers - one, two, three, and four [1 + 2 + 3 + 4 = 10] - and these written in dot notation formed a perfect triangle. http://www.american-buddha.com/pythagsource.1.gif Was used as a sacred symbol in Pythagorean society.

Tetractys also seen evident in Chinese, Kabbalists and etc, symbols. Likely coincidence. Cosmological belief that the planets moved in a musical (mathematically musical) harmony or rhythm. http://mathworld.wolfram.com/images/eps-gif/PythagoreanTheoremFigure_1000.gif http://www.grc.nasa.gov/WWW/k-12/airplane/Images/pythag.gif Legend has it that upon the completion of this theorem, Pythagoras sacrificed 100 oxen. http://www.geom.uiuc.edu/~demo5337/Group3/hist.html Euxdoxus:

200 years later found a way to deal with the 'unutterable' irrational numbers that the Pythagoreans discovered, but damned. More than 4000 years ago this concept was already known to the ancient Egyptians, Chinese, Indians and Babylonians. However, it is believed that Pythagoras was the first to prove it. http://ualr.edu/lasmoller/pythag.html Integers that satisfy the Pythagorean Theorem. http://www.geom.uiuc.edu/~demo5337/Group3/spiral.gif Euxdoxus Euclid Fermat http://www.math.utah.edu/~pa/math/flt.gif The sum of the angles of a triangle is equal to two right angles. Also, a polygon with n sides has sum of interior angles equal to 2n-4 right angles and sum exterior angles equal to four right angles. Solved equations by geometrical means The 5 regular solids. Taught that the Earth was a sphere at the center of the universe.

The orbit of the Moon was inclined to the equator of the Earth.

Realized that Venus was the same as an evening or morning star. http://jwilson.coe.uga.edu/EMAT6680/Parveen/golden16.gif Astronomy Greatly influenced religious belief that harmony ruled all; harmony of numbers, etc. And the inventions were so admirable, and so divinised by those who understood them, that the members used them as forms of oath: "By him who handed to our generation the tetractys, source of the roots of ever-flowing nature."

—Iamblichus, Vit. Pyth., 29 Much was due to the propaganda and zeal of the Pythagoreans. Part was also due to the lack of education of others. Therefore, Pythagoreans and Pythagoras was deemed elite and wise. Due to his semi-divine status, Pythagoras was often depicted as figure of authority or general admiration in art/paintings/murals Authority and mysticism come together making him rather influential. The influenced was mainly the Pythagoreans. It is said that he was often forced into political affairs due to his influence and wisdom. He chose to escape that for the most part. Was a sign of divinity.

Though this was untrue, it is likely that he had a large birthmark. To save a man, he bit snakes to death.

This was another semi-divine feat. It is said that his birth was prophesied and that he would be wiser than man. One writer, most likely trying to depict Pythagoras as a divine figure, told a story of:

Pythagoras walking in the city

he heard a puppy yelping

the puppy was being kicked by a man

he told the man to stop because the puppy was the reincarnation of the soul of his deceased friend Triangulation Trigonometry, whose fundamental principles are based on Pythagorean work, is used in triangulation technology and techniques.

ex: GSP Construction Easy integer construction of right angles and triangles are fundamental in construction for the triangle is the strongest shape.

An example of these uses is building struts and ties in roofs.

This basic and quick reference knowledge (such as the 3,4,5 triangle) is the basis of building and helped society focus on more complex problems. Shortest distance The converse Pythagorean theorem allows modern mathematicians or just people to find the shortest distance to a location.

This is also used the modern technologies like GPS. Engineering Oceanography

Meteorology

Geology

Aerospace

Electrical

Most if not everything electronic/electrical operates or was developed using the Pythagorean Theorem.

Engineering encompasses this because design these concepts.

Basically, any calculations using Trigonometry or logarithms used Pythagorean theorem. Having the fundamental principle: Pythagorean Theorem, allowed the development of fields like Trigonometry and Logarithms. This all allowed math to become more abstract. Physics Domain of abstract and practical applications of math and science.

Pythagoras was a segue to the development of abstract math or math as a liberal study. Metaphysics Domain of abstract and practical applications of math and science.

Pythagoras was a segue to the development of abstract math or math as a liberal study. Modern Society

as... More highly educated and technologically advanced society. Less religious and more scientific and spiritual. Platonism Rosicrucianism Aristotelian Classical philosophy Founded on Aristotle's beliefs and theories.

Idea of a group/brotherhood similar to the Pythagoreans; like minded thinkers grouped together. Claimed to have evolved from the Pythagoreans.

Opposed religious dogma.

Devoted to geometry/mathematics. Iamblichus Porphyry Diogenes Many historians are in conflict of just how influential Pythagoras was because of the lack of objective historical records. http://plato.stanford.edu/entries/pythagoras/ Both had strong agenda in favor of Pythagoras.

Claimed that all Greek Philosophers plagiarized from Pythagoras' ideas. Has written works on Pythagoras.

Had little objectivity. He was a student of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato. Not as great

no solid evidence of achievement

idea of person is influential Great

divine figure

enlightened

many accomplishments Not great

too much due to circumstance and perspective

The Pythagoreans as a group, due to THEIR accomplishments are considered greater Any man whose actions influenced by subsequent developments along quite a different course that would have been if followed if these actions had not been taken.

~ The Great Man Theory A man whose actions are the consequence of outstanding capacities of intelligence, will and character rather than of accidents of position.

~The Great Man Theory A perspective or bias.