...of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Since the fourth century AD, Pythagoras has commonly been given credit for creating the Pythagorean Theorem. The theorem dates back to Pythagorean triples found on Megalithic monuments from circa 2500 in Egypt and northern Europe incorporating right triangles with integer sides. The Middle Kingdom Egyptian papyrus Berlin 6619, written between 2000 and 1786 BC, includes a problem whose solution was a Pythagorean triple. Even though the theorem had been previously utilized by the Babylonians and Indians and no evidence shows that Pythagoras worked on or proved this theorem, he and his students are credited for constructing the first proof. Pythagoras was born between 580 and 572 BC on the island Samos of the coast of Greece. As a young man Pythagoras was advised to head to Memphis in Egypt to study with priests who were renowned for their wisdom. It may have been in Egypt that Pythagoras learned geometric principles that fueled the theorem named after him. Pythagoras later migrated to Croton, Calabria, Italy and established a secret religious cult very similar to the earlier Orphic cult. Toward the end of his life, Pythagoras fled Croton because of a plot against him and his followers, Pythagoreans, by a noble of Croton named Cylon. Pythagoras died in Metapontum between 500 and 490 BC around ninety years old from unknown causes. His studies and part in the Pythagorean Theorem...
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...Born during 570 BC on an island shaped as a peninsula called Samos, Pythagoras, the most well-known philosopher/ mathematician now in days, grew up with a wealthy family which provided him with an education. While growing, Pythagoras had many tutors and sophists that lead him to the path in which he took of math. At the age of 18, Pythagoras meets and got influenced extraordinary by a master of math and astronomy called Thales. Since back then, all the variety of science and math that we now have, were very limited due to the lack of scientific discovery. The main section of study before was philosophy, and years after, a cluster of subject’s appeared with the root word “logos” meaning the study of something that requires logic. Furthermore,...
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...the man who proved it. Pythagoras was born in 570 BC in Samos, Greece. His father, Mnesarchus, was a merchant from Tyre who traveled abroad. It is rumored that Pythagoras traveled with his father during his early years and was introduced to several influential teachers, including Thales who was a famous Greek philosopher. Several years and many countries later, Pythagoras found himself in Egypt. It was here that he studied at the temple of Diospolis and was also imprisoned during the Persian invasion. During the time he was imprisoned, Pythagoras began to study the religion called Zoroastrianism (Lauer/Schlager, 2001). It was because of these teachings and ideals that Pythagoras eventually moved to Italy. At age 52, while living in Croton, Italy, Pythagoras established the Pythagorean society. It was through this society and his positions in local government that Pythagoras recruited men and women in order to lead them to the pure life with his spiritual and mathematical teachings. Pythagoras believed that number was limiting and gave shape to all matter and he impressed this upon his followers (Gale, 1998). During his time leading the Pythagoreans, Pythagoras not only proved the Pythagorean Theorem, but also made other mathematical contributions. One of those contributions was that a number is an abstract entity, separable from all specifics. He also discovered that the sum of the angles in a triangle is equal to two right angles. While Pythagoras himself provided the world...
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... First American paperback edition published in 2006 by Enchanted Lion Books, 45 Main Street, Suite 519, Brooklyn, NY 11201 Copyright © 2002 Philip Stokes/Arcturus Publishing Limted 26/27 Bickels Yard, 151-153 Bermondsey Street, London SE1 3HA Glossary © 2003 Enchanted Lion Books All Rights Reserved. The Library of Congress has cataloged an earlier hardcover edtion of this title for which a CIP record is on file. ISBN-13: 978-1-59270-046-2 ISBN-10: 1-59270-046-2 Printed in China Edited by Paul Whittle Cover and book design by Alex Ingr A618C90F-C2C6-4FD6-BDDB-9D35FE504CB3 Philip Stokes A618C90F-C2C6-4FD6-BDDB-9D35FE504CB3 ENCHANTED LION BOOKS New York Contents The Presocratics Thales of Miletus . . . . . . . . . . . 8 Pythagoras of Samos . . . . . 10 Xenophanes of Colophon 12 Heraclitus . . . . . . . . . . . . . . . . . . . 14 The Scholastics St Anselm . . . . . . . . . . . . . . . . . . 48 St Thomas Aquinas . . . . . . . 50 John Duns Scotus . . . . . . . . . 52 William of Occam . . . . . . . . . 54 The Liberals Adam Smith . . . . . . . . . . . . . . 106 Mary Wollstonecraft . . . . 108 Thomas Paine . . . . . . . . . . . . . 110 Jeremy Bentham . . . . . . . . . 112 John Stuart Mill . . . . . . . . . . 114 Auguste Comte . . . . . . . . . . . 116 The Eleatics Parmenides of Elea . . . . . . . 16 Zeno of Elea . . . . . . . . . . . . . . . 18 The Age of Science Nicolaus Copernicus . . . . . . 56 Niccolò Machiavelli . . . . . . . 58 Desiderus Erasmus...
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...Pythagoras theorem Abstract Pythagoras theorem gives a relationship of the three sides of right angled triangles. It is extended to draw relationship among the interior angles of such right-angles triangles to form what is known as trigonometrical ratios. The theorem has vast application in science and mathematical phenomena. It is also used in the derivation of other theorems. This paper attempts to uniquely explain the theorem by experiment. Calculations and measurements will be done to arrive at stated proofs. I addition, theoretical values (value obtained through calculation) and practical ones are compared to establish the degree of error so allowed. Introduction Pythagoras theorem is mathematically expressed as So that c is the square root of the first two terms The sides as labeled are: a is the adjacent, b the opposite and c the hypotenuse. Therefore, the square of the hypotenuse is equal to the sum of the squares of the opposite and the adjacent. The adjacent can be called the base and the opposite the height of the triangle. These two sides are often referred to as the legs of the triangle and the hypotenuse as the longest side of the triangle. Relationships of the interior angles This is basically the trigonometrical ratios. Included angle is the angle enveloped by any two sides in the triangle. We use capital letters to denote the angles so that A is the angle included by band c. Similarly the rest will be B and C. stated otherwise, c corresponds...
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...ANAXIMANDER Anaximander (610 BCE - 546 BCE) was a Milesian School Pre-Socratic Greek Philosopher. Like most of the Pre-Socratics, very little is known of Anaximander’s life. He was born, presumably in 610 BCE, in Ionia, the present day Turkish west coast, and lived in Miletus where he died in 546 BCE. He was of the Milesian school of thought and, while it is still debated among Pre-Socratic scholars, most assert that he was a student of Thales and agree that, at the very least, he was influenced by his theories. He is infamously known for writing a philosophical prose poem known as On Nature, of which only a fragment has been passed down. In that fragment Anaximander innovatively attributes the formation of a regulating system that governs our world, the cosmos. Furthermore, he put forth the radical idea that it is the indefinite (apeiron), in both the principle (archē) and element (stoicheion), from which are the things that are. In addition to such ingenuity, Anaximander also developed innovative ideas and theories in astronomy, biology, geography, and geometry. For Anaximander, the origination of the world could not be reduced to a single element or a collection of elements alone. Rather, one needed to understand that the origin was in both principle and element not definable in a definite sense or attribution. While this was a radical perspective in relation to the more determinate theories of others from the Milesian school, it does seem to have some derivation from older...
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...Term Paper On Role of the Pythagoras in the field of mathematics Business Mathematics code Submitted By Team Harmony 1. Faisal Enayet (B1506003) 2. HafijulHasan (B1506007) 3. Plato Khisa (B1506035) 4. FarhanajAnchal (B1506075) 5. K.HusFariha (B1506120) 6. SumaiyaMeher(B1506155) Submitted To Lecturer AKTER KAMAL Business Mathematics Bangladesh University of Professionals Submission on Date: 02/05/2016 BBA 2015; SEC- C LETTER OF TRANSMITTAL 02 may 2016 Akter Kamal Lecturer Faculty of Business Studies Bangladesh University of Professionals Subject: Submission of term paper on “The role of Pythagoras in the field of mathematics” Respected Sir, We the students of BBA, section C, we are very glad to submit you the term paper on the topic of “The role of Pythagoras in the field of mathematics” that you asked us to submit, which is a part of our course requirement. For the purpose of completing the term paper we did a simple research on the provided topic. We have completed our research and assessment on our term paper topic according to your specification and regulation. We have tried our best to gather information according to the requirements and our ability. There may be a few mistakes, because we are still beginner in this line of work but we hope that in future this term paper will remind us not to make the same mistakes again and so this will become a great learning in experience. At last, we would like to thank to you...
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...| Greeks | CHAPTER 1 CHAPTER 1 Chinese | Indians and Hindus | Islam | God | Ancient Greek theology was polytheistic, based on the assumptions that there were many gods and goddesses. | The idea of Heaven (T’ien) plays a prominent role in indigenous Chinese religion. The term can refer to a god, an impersonal power, or both. The concept Is now well-defined, and religious scholars have had a difficult time deciding whether T’ien was believed to be a force like fate or a personal identity. It is also unclear whether the ancient Chinese believed T’ien responded to human supplication or simply worked in accordance with the principles of T’ien. | God created human beings and everything. | Monotheism, belief in one God, is the most important and foundational concept in Islam. Muslims believe in one God who created the universe and has power over everything within it. He is unique and exalted above everything. He creates, and His greatness cannot be compared to His creation. | Man | Men had the dominant role in public life in ancient Greece. They were engaged iin politics and public events, while women were often encouraged to stay in the home. | For the Chinese then, Philosophy is the translation of words into action or the application of theory into praxis. Thus for the Chinese, philosophy singles out a person to live on what he says/teaches thus, a man/woman of integrity who has word/s of honor. | In Hindu tradition, Manu is the name accorded to a progenitor of humanity...
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...Running head: GREEK PHILOSOPHY Greek Philosophy Cherese Howard HUM 100 November 03, 2009 Felix Figueroa Greek Philosophy Greek Philosophy is a great civilization that is very much still a part of our culture and everyday living of today. These great men discovered things that were too advance for their life time. Without them, society of today will not have geometry, logic or natural sciences. The term philosophy is Greek in origin meaning “love of wisdom.” (Owens, 2003) Pythagoras suggested that “wisdom is something divine and man cannot be truly wise but a lover of wisdom.” (Owen, 2003) Greek philosophy began around 1200 B.C.E. Historians believe that it was born on the south-west coast of Turkey, in a city-state called Milatos. This was near the end of the Minoan period which did not make it past the Bronze Age civilizations. The city was then refounded by Ionian Greeks in the eleventh century B.C.E. Historians also believed that a young man from Miletus was one of the founding fathers of Natural Greek Philosophy, which questions “nature and the natural causes of what occurs in the cosmos.” (Beginnings of Greek Philosophy, pg 240) Thales believed “that everything is the world is made up of matter which might take various forms like solid, liquid, or a gas.” (Beginnings of Greek Philosophy, pg 240) He knew that water could take on all three forms. Thales knew that he could take a piece of ice and apply heat to it and it will turn into water...
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...Demo Speech November 2, 2010 Topic: Magic square personal yantra Specific Purpose Statement: By the end of my speech, my audience will know how to make their own personal yantra by way of a magic square. Thesis Statement: Knowing your personal yantra is an interesting way to gain insights of your character and life’s path. I. Introduction A. Attention- Getter: Who hasn’t wondered, what is the purpose of life? 1. Who hasn’t thought to themselves, what will my life be like in the future? 2. Will I be happy? 3. What about my family and friends? 4. Have you ever wondered if you will be rich. B. Reason to Listen: Well what if I told you, there was an easy way to answer some of life’s most interesting questions. 1. That simple mathematically equations can decipher your fate. 2. That there is a reason why you are who you are. 3. A way to obtain your ideals about love, money and career. C. Credibility Statement: The ancient tradition of creating numerical yantras has been around for 5 thousand years. 1. I found numerous resources concerning numerology. a. Including Richard Webster’s Numerology Magic , that I got from the library. b. There are also plenty of websites dedicated to numerology. 2. I personally have created many yantras for my friends and family. D. Personal yantras are not only fun to construct, but perhaps can give a person some insight on the purpose of their lives. E. Today, I am going...
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...TRUE & FALSE 1. Zeno, Miletus, and Elea are presocratic philosophers. 2. The presocratics were introduced to, but rejected, early Christianity. 3. Believing something because you want it to be true is the same as believing something on the basis of evidence. 4. The presocratics broke decisively from their predecessors. 5. According to Thales, all is air. 6. Anaximander sees changes in the world like they are a type of justice being served. 7. Zeno’s paradoxes were regarded as trivial by those who came after him. 8. The aim of the “two rows” or “blocks” paradox is to show that motion is impossible. 9. Parmenides argues that there is one fundamental kind of change. 10. The Milesians adopt a common strategy, differing only in how they carry it out. * 1. On Plato’s view, a shadow of a feather is more real than the feather. 2. Plato’s metaphysical ideas can be summed up in the phrase “seeing is believing.” 3. Plato says that there are some things that last forever. 4. The parable of the cave illustrates the way Plato understands the learning process. 5. Plato’s line in the simile of the line is divided into four equal parts. 6. The shadows on the wall of Plato’s cave represent the forms. 7. A realist believes that there are mind-independent entities, while an idealist does not. 8. Plato is a realist. 9. Forms are the entities that Plato believes to exist...
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...As much as I favorite Heraclitus for his obscure, negative outlooks, and mysterious sayings, I would have to say that Thales of Miletus (in my opinion), has the most compelling ideas and philosophies in the pre-Socratic ages. He was usually credited for being the first systematic philosopher of the Western World. He believed that there was an explanation for everything instead of believing/ promoting supernatural causes. "Aristotle, the major source for Thales's philosophy and science, identified Thales as the first person to investigate the basic principles, the question of the originating substances of matter and, therefore, as the founder of the school of natural philosophy. Thales was interested in almost everything, investigating almost all areas of knowledge, philosophy, history, science, mathematics, engineering, geography, and politics." (Thales of Miletus, http://www.iep.utm.edu/thales/) He often developed logical, geometrical theories, such as devising some that allowed hi to measure the height of the pyramids from the ground, and used his intelligence and understanding of the world to predict crop outcomes, and be very profitable at it. It is also pretty interesting to find out that he was technically the first person to study electricity. "LORDZB" states, "It had been noticed that amber, when rubbed, attracted threads of fiber to it. It was this static electricity which Thales’ studied. When the negative particle of the atom was named it was called...
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...Edexcel GCSE Mathematics (Linear) – 1MA0 PYTHAGORAS THEOREM Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Items included with question papers Nil Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided – there may be more space than you need. Calculators may be used. Information The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed – you should take particular care on these questions with your spelling, punctuation and grammar, as well as the clarity of expression. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. 1. PQR is a right-angled triangle. PQ = 16 cm. PR = 8 cm. Calculate the length of QR. Give your answer correct to 2 decimal places. ............................... cm (3 marks) 2. X 3.2 cm Y Diagram NOT accurately drawn 1.7 cm Z XYZ is a right-angled triangle. XY = 3.2 cm. XZ = 1.7 cm. Calculate the length of YZ. Give your answer correct to 3 significant...
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...QUIZ #1 NOTE: Be sure to answer each question in complete sentence. Be sure to proofread your answer for correctness in grammar, spelling, punctuation mark, etc. Your answer must be word-processed, double-spaced (repeat, double-spaced), with 10-12 font size. Be sure to write your NAME and ID number in your paper. 1. Differentiate between: a. Ethics and Aesthetics Ethics constitutes the difference between right and wrong.Ethics are usually more broad and informal than laws, they are usually taught in ones childhood. Aesthetics is a branch of philosophy that emphasizes on the beautiful and the ugly. It can be defined as the study of the mind and emotions in relation to the sense of beauty. b. the rationalist and the empiricist (at least 3 differences) A rationalist may study the principles of philosophy, theology, and architecture. An empiricist relies on observation, experiment, and conclusions. c. metaphysics from epistemology Metaphysics is the branch of philosophy that treats principles. It also includes ontology and cosmology, and is connected with epistemology. Epistemology is the search for knowledge, validity, and methods. d. Axiology and ethics Axiology is the study of value. It is to research the nature, criteria, and metaphysical status of value. Ethics differs from the study of value given that it relies on what is right and wrong. Each individuals ethics will differ. Whereas Axiology is the current status of a particular value. e. Axiology and Aesthetics ...
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...ByZantine Music culture Body What is known today as Byzantine music has been developed and refined for over two millennia. With its earliest roots going back to Pythagoras' philosophy on the division of chords, its latest and final revision took place in 1881 in the city of Istanbul; the city still referred to by the practitioners of this complex art by its more ancient name of Constantinople. For the purposes of this essay, the name Constantinople will refer to the city up to and including the present day. To provide for a clearer understanding of the theory of Byzantine music, the process of the development of Byzantine music as it is known today will be divided into two eras. We will call these two eras pre-Byzantine, and Byzantine periods of musical development. The pre-Byzantine part of the essay will cover developments made before the foundation of Constantinople. This period includes everything before c. 330 C.E. The Byzantine period will include all of the advancements made after the founding of Constantinople and the Byzantine Empire. Every refinement made up to the present day, the most important dates being the simplification of the notation in 1821 by John Koukouzeles and the great council of 1881, will be included in this period, but not, unfortunately in the essay. Although there is a very significant part played by notational theory on the development of Byzantine music theory and Hymnography, the scope of this essay does not allow for us to delve into...
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