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Pythagoras's Theory of Harmony of the Spheres - Pythagoras is considered, not only as one of the greatest mathematicians in history, but also for his works concerning music, philosophy, astrology, and many others for all the discoveries made by him. One of the greatest discoveries attributed to Pythagoras is the discovery of the musical scale used nowadays. This scale was based on the principle in which all Pythagoreans base their thought: the existence of numbers in every single aspect in existence. A philosophical belief of universal creation based upon the perfect harmony between numbers and nature....   [tags: Pythagoras, philosphy, the republic]
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The Genius that Was Pythagoras - ... So since Pythagoras never wrote things down we will never know if Pythagoras really came up with the ideas he was credited for or if it was just one of his students work from his Pythagorean School. Also in my research I saw that over a 1,000 of years before Pythagoras was finding the hypotenuse of a triangle people in Mesopotamia were writing in cuneiform on their clay tablets doing the Pythagorean Theorem to find the area of their farmland. These tablets show proof that Babylonians had more practical as well as more advanced math and how experienced they were with numbers....   [tags: influential antient Greek mathematicians]
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The Genius that Was Pythagoras - ... [2] The society that he created, while bene cial at the time, has over the years tainted his mathematical ndings to a point where we must question whether or not he actually discovered the theorems that many people believed he did. This was due to the fact that his society shared ideas and intellectual discoveries among the group members, and individual credit for each theory was not given out at the time. Because of this fact, it is dicult to determine whether the theories attributed to Pythagoras were actually his, or rather an e ort from the group that he created....   [tags: Ancient Greek mathematicians] 1443 words
(4.1 pages)
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Pythagoras and Plato - For the Greeks philosophy wasn’t restricted to the abstract it was also their natural science. In this way their philosophers were also their scientist. Questions such as what is the nature of reality and how do we know what is real are two of the fundamental questions they sought to answer. Pythagoras and Plato were two of the natural philosophers who sought to explain these universal principles. Pythagoras felt that all things could be explained and represented by mathematical formulae. Plato, Socrate’s most important disciple, believed that the world was divided into two realms, the visible and the intelligible....   [tags: Philosophy ]
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A Brief Biography of Pythagoras - ... 3. Areas of Mathematical Work Pythagoras studied many different fields of scholarly studies. Because of the influence of his teachers, Pythagoras was mainly known for studying and working in the field of mathematics. In this field, Pythagoras mostly focused on geometry, where his main contribution to mathematics can be found. This contribution is known as the Pythagorean Theorem. The Pythagorean Theorem is an equation that can help mathematicians find one side of a triangle by either adding or subtracting the length of the other two sides, depending on which side of the triangle needs to be found....   [tags: ancient greek philosophers, mathematicians] 914 words
(2.6 pages)
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Pythagoras' Invention of the Pythagorean Theorem - ... To solve this equation, place 3^2 to the right side, which makes it negative. The equation then become this: b^2=5^2-3^2. After subtracting the squares of 5 and 3, you get b^2=16 . Then if you root 16 (√16), you get 4, therefore b=4. And a new form of the theorem appeared: b^2=c^2-a^2. If you do some rearrangements, a^2=c^2-a^2 also works the same. Generally, the Pythagorean Theorem works with different form of algebraic equations by rearranging a^2+b^2=c^2, to solve different cases. Pythagoras made proofs to prove that is theorem is always correct and goes to all right-angled triangles....   [tags: triangle, hypotenuse, equation] 1065 words
(3 pages)
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Pythagoras’ Impact in Geometry - ... The followers were men and women also known as mathematikoi. The theories and ideas in mathematics that his followers made were accredited to him. They were also a very secretive group, so not much is known how they came up with their ideas and philosophies. (Douglas, 2005) He died in approximately 500 B.C. and his followers, “continued to work for at least 50 years afterward.” (Simonis 168, 1999) Pythagoras was very interested in the relationship of numbers and their importance in the world....   [tags: triangle, greece, mathematics]
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Pythagoras and His Contributions to Modern Mathematics - Pythagoras is truly a man unlike any other throughout history. Perhaps his greatest achievements are within the realm of mathematics; with his greatest known theory being the Pythagorean Theorem. His theory is so well known that even today it peaks the interests of many mathematicians, with more than 400 proofs being spawned off of his original theorem. Though his theorem is common knowledge in this modern age, his life still remains a mystery to most, similar to most pre-Socratic philosophers....   [tags: Mathematics, Biography, Pythagorean Theorem]
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Pythagoras of Samos -      Pythagoras of Samos is a man who was more than just a mathematician. A Greek philosopher, founder of the Pythagorean brotherhood, he was an extremely important political figure for his time. He invented vegetarianism and created one of the first secret organizations. Not much is known about his mathematical achievements because he never wrote anything down. It is unsure where his views end and his disciple’s views began. He influenced Plato and Aristotle and made contributions to the development of mathematics and western philosophy....   [tags: Greek Biographies Bio essays research papers]
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Pythagoras - Pythagoras Pythagoras was born around 569 B.C. in Samos, Ionia, and died around 475 B.C. Pythagoras was a Greek philosopher, and mathematician. Pythagoras also developed the Pythagorean brotherhood. This was religious in nature, however it formulated principals that influenced the thoughts of Plato and Aristotle, and contributed to the development of mathematics and Western rational philosophy. Pythagoras not only developed the theorem of A2+B2=C2, but he was also the first to create the music scale of today....   [tags: Papers] 473 words
(1.4 pages)
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Pythagoras - Pythagoras Pythagoras was a Greek philosopher that was responsible for some devolpments in mathematics. He was born around 560 B.C. and died around 480 B.C. He was originally from the city of Samos, Ionia(Later day Italy), but moved away from his home to escape the tyranny of Polycrates. Ionia was an area around the Mediterranean Sea and Samos was an island inside that area. From Samos he moved to the city of Croton. In Croton he established a school. The school was a philosophical and religious school....   [tags: Papers] 343 words
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Pythagoras - Pythagoras My name is Pythagoras of Samos. I believe I should win the fabulous two-week cruise on the incomparable Argo because I dedicated my life to educating and caring for the future generations. I risked my life to share my knowledge with anyone who wanted to learn. I was born on the island of Samos, but lived most of my life in Crotona, Italy. When I was a young man, I traveled to many different places to observe the different lifestyles and cultures. Some of the countries I visited were India, Egypt, and Persia (Bulfinch)....   [tags: Papers] 614 words
(1.8 pages)
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Mathematics Coursework - Beyond Pythagoras - Mathematics Coursework - Beyond Pythagoras 1) The numbers 3, 4, and 5 satisfy the condition 3² + 4² = 5² because 3² = 3x3 =9 4² = 4x4 = 16 5² = 5x5 = 25 and so 3² + 4² = 9 + 16 = 25 = 5² I will now have to find out if the following sets of numbers satisfy a similar condition of (smallest number) ² + (middle number) ² = (largest number) ². a) 5, 12, 13 5² + 12² = 25 + 144 = 169 = 13² b) 7, 24, 25 7² + 24² = 49 + 576 = 625 = 25² 2) Perimeter ============ [IMAGE] 5 5 + 12 + 13 = 20 12 [IMAGE] 7 7 + 24 + 25 = 56 24 b) Nth term Length of shortest side Length of...   [tags: Papers] 1389 words
(4 pages)
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Beyond Pythagoras - Mathematical Investigation - Beyond Pythagoras - Mathematical Investigation 1) Do both 5, 12, 13 and 7, 24, 25 satisfy a similar condition of : (Smallest number)² + (Middle Number)² = (Largest Number) ² . 5, 12, 13 Smallest number 5² = 5 x 5 = 25 Middle Number 12² = 12 x 12 = 144+ 169 Largest Number 13² = 13 x 13 = 169 7, 24, 25 Smallest number 7² = 7 x 7 = 49 Middle Number 24² = 24 x 24 = 576+ 625 Largest Number 25² = 25 x 25 = 625 Yes, each set of numbers does satisfy the condition....   [tags: Papers] 1522 words
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Beyond Pythagoras Math Investigation - Beyond Pythagoras Math Investigation Pythagoras Theorem: Pythagoras states that in any right angled triangle of sides 'a', 'b' and 'c' (a being the shortest side, c the hypotenuse): a2 + b2 = c2 [IMAGE] E.g. 1. 32 + 42= 52 9 + 16 = 25 52 = 25 2. 52+ 122= 132 3. 72 + 242 = 252 25 + 144 = 169 49 + 576 = 625 132 = 169 252 = 625 All the above examples are using an odd number for 'a'. It can however, work with an even number. E.g. 1. 102 + 242= 262 100 + 576 = 676 262 = 676 N.B....   [tags: Papers] 1011 words
(2.9 pages)
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Investigating Pythagoras - Investigating Pythagoras Introduction ============ [IMAGE]For this piece of work I am investigating Pythagoras. Pythagoras was a Greek mathematician. Pythagoras lived on the island of Samos and was born around 569BC. He did not write anything but he is regarded as one of the world's most important characters in maths. His most famous theorem is named after him and is called the Pythagoras Theorem. It is basically a²+b²=c². This is what the coursework is based on. I am going to look at the patterns, which surround this theorem and look at the different sequences that can be formed....   [tags: Papers] 3477 words
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Pythagoras' Theorem - Pythagoras' Theorem I am going to study Pythagoras' theorem. Pythagoras Theorem is a2 + b2 = c2. 'a' being the shortest side, 'b' being the middle side and 'c' being the longest side (hypotenuse) of a right angled triangle. For example, I will use 32 x 42 = 52 . This is because: 32 = 3 x 3 = 9 42 = 4 x 4 = 16 52 = 5 x 5 = 25 So.. 9 +16 = 25 For this table, I am using the term a, b, b + 1 Triangle Number (n) Length of shortest side Length of middle side Length of longest side Perimeter Area 1 3 4 5 12 6 2 5 12 13 30 30 3 7 24 25 56 84 4 9 40 41 90...   [tags: Papers] 675 words
(1.9 pages)
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Beyond Pythagoras - Beyond Pythagoras What this coursework has asked me to do is to investigate and find a generalisation, for a family of Pythagorean triples. This will include odd numbers and even numbers. I am going to investigate a family of right-angled triangles for which all the lengths are positive integers and the shortest is an odd number. I am going to check that the Pythagorean triples (5,12,13) and (7,24,25) cases work; and then spot a connection between the middle and longest sides....   [tags: Papers] 919 words
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Pythagoras Experiment - Pythagoras Experiment Aim: To investigate the relationships between the lengths of the 3 sides of the right angled triangles and the perimeters and areas of these triangles. Task 1: a) The numbers 5, 12, 13 satisfy the condition. 5² + 12² = 13² Because 5² = 5x5 = 25 12² = 12x12 = 144 13² = 13x13 = 169 And so 5² + 12² = 25 + 144 = 169 = 132 b) The Numbers 7, 24, 25 also satisfy the condition. 7² + 24² =25² Because 7² = 7x7 = 49 24² = 24x24 = 576 25² = 25x25 = 525 And so 7² + 24² = 49+ 576 = 625 = 25² Task2: The perimeter and area of the triangle are: Perimeter = 5 + 12 + 13 = 30 units Area = ½ x 5 x 12 = ½ x 60...   [tags: Papers] 1227 words
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Beyond Pythagoras Investigation - Beyond Pythagoras Investigation In this investigation, I am trying to find the rules and patterns for right-angled triangles. Each length of the right-angle triangle is going to be a positive integer, and the shortest length is going to be an odd number. Below is a typical type of a Pythagoras triple equation: [IMAGE] Formula:a² + b² = c² 3² + 4² = 5² 9 + 16 = 25 In this equation, the first step I took was to put the numbers instead of the letters. Once I did that I squared all the numbers, and when I add a² + b² it equaled to c²....   [tags: Papers] 4849 words
(13.9 pages)
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The Divine Number - ... This gigantic effigy on the outskirts of Cairo shows the mysterious thought-process of the Egyptians. To make these megalithic buildings, with technology would pose as a challenge to anyone, but the Egyptians managed to succeed without anything near to the advanced technologies we have today. These masterpieces were observed by millions of people, including the one and only Pythagoras. Pythagoras is one of the math world’s greatest icons, and for understandable reason. Without Pythagoras, we would not have geometry, calculus, and many other important forms of math....   [tags: pythagoras, ancient egyptians, cultures]
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Tracing Changes in Pythagoras' Speech in Ovid's Metamorphoses - Tracing Changes in Pythagoras' Speech in Ovid's Metamorphoses   Change in Ovid, as well as in life, seems to be the only constant.   Change is the subject of the Metamorphoses and Ovid's purpose in recounting myths is established from the very beginning: "My intention is to tell of bodies changed to different forms... with a poem that runs from the world's beginning to our own days" (1.1-4).  From this foundation, Ovid launches into his stories, using metamorphosis more as a vehicle for telling his stories than as an actual subject matter.  Although he retells religious myths, Ovid is not writing a religious manuscript.  Rather, the product is a work of literature.  Ovid is conscious tha...   [tags: Ovid Metamorphoses Essays]
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Pythagora's Contributions to Math - Pythagoras was a mathematician who has influenced the math culture until this day. His studies in math are more noted than his contributions to philosophy as well as religion. Due to the fact Pythagoras lived between roughly 520-495 bc there is very little information about him. In fact his exact birthday and death date are mainly estimations based on other historical events. Whatever we know about him is information learned after his death. Most of his writings were not published so we do not have many of his personal notes....   [tags: ancient Greek mathematicians] 1075 words
(3.1 pages)
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Pythogoras of Samos - Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know little about his achievements. There is nothing that is truly accurate pertaining to Pythagoras's writings. Today Pythagoras is certainly a mysterious figure. Little is known of Pythagoras's childhood. Pythagoras's father was Mnesarchus, and his mother was Pythais. Mnesarchus was a merchant who came from Tyre. Pythais was a native of Samos. As a child Pythagoras spent his early years in Samos, but traveled with his father....   [tags: essays research papers] 1344 words
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The Ancient Greeks That Made a Difference For Today - A majority of the mental and physical tools we use and apply today are founded in the work of the ancient Greeks. The mathematicians, engineers and scientists Pythagoras, Euclid, Archimedes, and Thales developed the knowledge, theories and ideas in which we live our lives today. Pythagoras plays a major part in modern day mathematics. Discovering a way to make “order out of chaos”, he was “often referred to as the first pure mathematician.” Born on “the island of Samos … in 569 BCE,” Pythagoras was “well educated.” Individuals known as Pythagoreans admired Pythagoras’ knowledge, and “taught other people what he had taught them” including everything Pythagoras believed to be true, and everyt...   [tags: mathematics, science, astrology] 1020 words
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Pythagorean Philosophy and its influence on Musical - Fundamentals of Musical Acoustics. New York: Dover Publications Ferrara, Lawrence (1991). Philosophy and the Analysis of Music. New York: Greenwood Press. Johnston, Ian (1989). Measured Tones. New York: IOP Publishing. Rowell, Lewis (1983). Thinking About Music. Amhurst: The University of Massachusetts Press. "Music is the harmonization of opposites, the unification of disparate things, and the conciliation of warring elements...Music is the basis of agreement among things in nature and of the best government in the universe....   [tags: essays research papers] 1342 words
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The History And Contributions - Greek Geometry Although the original roots of geometry can be traced to the Egyptians, the Greeks built on most Egyptian theories that we use today. Greek astronomy and Greek geometry were both used in order to answer many difficult questions of the time. Without geometry, the study of astronomy would have been almost impossible, and vice versa. Even though many Greek theorems and principles were later built on by geniuses such as Einstein and Lobachevsky, the basis still remains the same. The development of Greek geometry is said to be started by Thales of Miletus....   [tags: essays research papers] 531 words
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The Influence of Greek Thought on Modern Science and Mathematics - The Influence of Greek Thought on Modern Science and Mathematics Parallels can be drawn from Greek thought and compared to today’s modern world views. This comparison also brings forth the influences of the Greek philosophies to the world’s contemporary aspects. More specifically, mathematics and science elicit the relationships of the ancient Greek beliefs and the existing theories and truths. Mathematics, as it relates to the Greek era and the present time, had created and still creates a very new approach to the thoughts of the mechanics of nature....   [tags: Philosophy] 612 words
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Accoustic Science: The Epitaph of Seikilos - ... Then at the appositive end of the frame two finger sized pieces of wood or bone were connect at their ends to make the pieces of wood produce at clapping sound. This instrument was used by dancers in the worship of Dionysus and Kybele the rattles were also used by Hercules to frighten away the Stymphalian Birds during his Sixth Labor. Kymvalon was made from metal version of Krotalon. This instrument’s main purpose was to worship Dionysus. Seistron was an early from of modern rattle .It consisted of a handle and U-shaped frame that had either moving parallel rods (striking in its walls), or constant rods with moving perforated noise-making objects....   [tags: muses, greek music] 1346 words
(3.8 pages)
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The Socratic Movement - In this essay, I will discuss one of the four major philosophical movements in Ancient Greek Philosophy; namely the Socratic movement. The Socratic turn was a philosophical shift from a natural to a social philosophy. It was a part of Ancient Greek philosophy which set in motion a huge movement of thought that influenced the course of mankind for many centuries. I will attempt to express my observations of this movement as clear and specific as possible. Social philosophy, also described as the philosophical study of social behavior (particularly in humans) was one of the key aspects of Plato’s philosophy....   [tags: Philosophical Movements, Ancient Greek]
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Analysis of Raphael´s Painting The School of Athens - The School of Athens (Figure 1) is a fresco painting–a painting done in sections in the fresh plaster–on one of the four walls of the room, the Stanza della Segnatura this room is designated as papal library in the Vatican palace. In this image Raphael represents pictorially the intellectual activity of philosophy. He chooses to represent philosophy by depicting a large number of philosophers in the midst of their activities. The fifty-eight figures who occupy the grandiose architectural space are depicted in the midst of their activity: they are questioning, arguing, demonstrating, reading, and writing....   [tags: greek, tradition, figures] 1805 words
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The Differing Perspectives of Greek Philosophers - ... Heraclitus and Parmenides both recognized that the materials which make up the universe could be broken down to one basic substance, but they came to disagreement over what that basic substance was exactly, as well as the state of being. Heraclitus believed that everything was fire (or made of fire), and that it was the fundamental source of change in the universe because a main property of the universe was that it was in a constant state of changing. Parmenides argued that the entire idea of change was impossible and that the universe was essentially unmoving and unchanging....   [tags: change, substance, knowledge] 1350 words
(3.9 pages)
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Understanding the Codes of Life - Numbers, or 5342591, are everywhere. The world of numbers expands every year it continues to exist. It diffuses past the very reaches of our imagination too big to even count, no pun intended. Numerology is the study of numbers and how they affect daily lives and situations. The world and all it makes up is made up of numbers, and these numbers help uncover the traits and characteristics of those corresponding to them. “...humankind has always been aware of the forces of cycles and nature. These natural cycles and cosmic rhythms exert an influence on every living organism.” (Crawford) How is everything made of numbers....   [tags: Numerology, Personology]
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Ontology of Mathematics - An ontological theorist generally begins his discussion with a preconceived notion of what kind of thing an object will turn out to be. Instead, we will here begin with a Thomassonian approach to the ontology of mathematics. First, let us consider what happens when we rst come to determine a mathematical proposition (which I will use synonymously with 'mathematical entitty'). A mathematician does not feel as though he creates mathematical theories. Pythagoras can hardly be thought to have created the claim that a2 + b2 = c2....   [tags: Mathematics]
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An Innovative Real-time Distance Estimation Method for Distance-only navigation of a Mobile Robot - Abstract— Autonomous mobile robots have been employed in wide applications in human life such as industry, disasters, military, and security. Meanwhile, robot secure navigation and guidance toward targets became an attractive subject for researchers. In most recent navigation methods, both the line-of-sight angle and the relative distance between the robot and target are assumed to be available. On the other hand, some navigation algorithms are based on distance information. For example, Equiangular Navigation and Guidance (ENG) law is a range-only navigation law....   [tags: Research Analysis ]
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Essential Tool for Musicians: The Circle of 4th’s and 5th’s - ... Just like Pythagoras made it, the Circle of fourths and Fifths is divided up into 12 places, like the numbers 1-12 on a clock. The Circle of fourths and Fifths helps you figure out what sharps or flats will occur in what key. The name of the key that is being played is the letter on the outside of the Circle,those are the major key. If you want to figure out how many sharps are in each key, count clockwise from C at the top of the Circle. The C major at the top is neutral so it does not have any sharps or flats....   [tags: Phythagoras, ] 848 words
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The Outbreak of Natural Philosophy from Religion - The Outbreak of Natural philosophy from Religion Science was not as prominent as it is now before, some people rejected science and all it had to offer for a long time. This was primarily because of the fact that people did not want to change their belief, not only theirs but their previous generations had believed in this also. This religious dogma they had believed in all their life, it was not until about the scientific revolution in the 16th century that science was widely accepted by all....   [tags: Philosophy] 2599 words
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Greek Culture and its Influences Today - “Greek civilization is alive; it moves in every breath of mind that we breathe; so much of it remains that none of us in one lifetime could absorb it all.” Ancient Greeks are known to be one of the greatest and most advanced people and have left behind a legacy that helped define the Western civilization. Cultural diffusion helped spread Greek culture all over the world, and its effects can still be felt today in almost every aspect. Greek culture has greatly affected different parts of my daily life including architecture, food, government, inventions, music, religion, and education....   [tags: Ancient Greece]
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The Relationship between Mathematics and Music - ... Although music is advancing due to different technologies becoming available, music tends to stay the same within cultures. Music is seen as a tradition in various cultures. For example, some cultures have a 5 note scale, others follow have an 8, while today, much modern music is written to what is known as a 12 note chromatic scale. Music has evolved over time adding more and discovering more ways that math is related to music. Once the Pythagorean was developed it was soon learned there still needed to be another tuning system....   [tags: geometry applied]
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The Neoplatonist Roots of Sufi Philosophy - The Neoplatonist Roots of Sufi Philosophy Neoplatonism strongly influenced the development of Sufism. Neoplatonism, as developed by Plotinus conceives God to be the source and goal of everything. Islam qua institution is closed to all critical and philosophical thought, but Sufism enjoys a more liberal and critical approach. It is probable that the translations of Plotinus have provided the necessary philosophical ground for Sufism. An examination of both Sufism and Neoplatonism reveals close similarities with regard to the nature of God, the soul, the body, concepts such as goodness, evil and beauty, death and life, and creation....   [tags: Philosophers Religion Papers] 2391 words
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Thales was the First Recorded Philosopher from Miletus - ... For him, water was too “concrete” of an object to be divine. In addition, remaining opposite elements triumphs water. Anaximander reasoned even if water were reality, it lacks in areas that makes it unable to be divine. Apeiron is an indefinite reality that is beyond the fixed matters on Earth. Anaximenes rejected this theory. In turn he contradicted that physics translated into objects surrounding us. The concept of aer does not refer to the air we breath rather a thick mist containing two processes: rarefaction and condensation....   [tags: water, condensation, atom] 585 words
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Ancient Athens of Greece - Ancient Athens of Greece Ancient Greece, is a civilization that still influences society today. Athens was one of the most important and powerful cities in Greece. The name Athens in Ancient Greek was Athenai. The Greeks believed that each city-state in ancient Greece had a god or goddess in charge of it, their special patron. Athens was named after Athena, the goddess of wisdom. The people of Attica chose Athena because of her gift, the olive tree. The Olive tree symbolizes peace and plenty. Ancient Athens influences society by the way government is ran, the philosophies used in sciences and mathematics, and arts that inspire actors and writers today....   [tags: democracy, greek theatre, philosophy]
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History of the Piano - The piano is an instrument that can be traced back through the centuries; there are no debates about that statement. Nevertheless, there are several different views on what begins the history of the piano. In his book, Pianos and their Makers, Alfred Dolge begins with the Monochord in 582 B. C., which was used by Pythagoras. However, Ernest Closson begins his History of the Piano with the clavichord and gives only five paragraphs to the influences from before. Everyone has their own interpretation of what the history of the piano is; however an instrument is just a piece of mechanical parts without the music that was played on it....   [tags: instrument, drums, square piano]
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Mathematical Investigation - Mathematical Investigation Pythagoras was a great mathematician who created theorems and one of his famous theorems was the "Pythagoras Theorem". You start with a right-angled triangle. The hypotenuse is labeled "c". The bottom of the triangle is "b" and the side of the triangle is labeled "a". [IMAGE] Pythagoras Theorem says that in any right angled triangle, the lengths of the hypotenuse and the other two sides are related by a simple formula. So, if you know the lengths of any two sides of a right angled triangle, you can use Pythagoras Theorem to find the length of the third side: Algebraically: a2 + b2 = c2 The numbers 3, 4 and 5 satisfy the condition...   [tags: Papers] 3909 words
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A Comparison of The Aeneid and Metamorphoses - A Comparison of The Aeneid and Metamorphoses      Both Vergil and Ovid imbedded underlying meanings in their epics The Aeneid and Metamorphoses.  In this paper I will focus on the underlying meaning in the Underworld scene in Vergil's The Aeneid (lines 356 through 1199).  I will also focus on three scenes in Ovid's Metamorphoses.  Both epics contain a larger message about the importance of the Roman past for its present and future under Augustus.         The story of Aeneas in the Underworld can be interpreted as a brilliant rendition of the story of Rome's past, present, and future.  When Aeneas descends into the Underworld, he is escorted by the Sibyl (lines 347 -...   [tags: comparison compare contrast essays]
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Fermat's Last Theorem - Rationale: The pythagorean theorem is a simple equation that has been taught to pupils from the beginning of middle school. a2+b2=c2 is the basic formula to calculate any one of the sides on a right angle triangle. Although starting with basic reinforcement for use of this theorem, usages of this theorem escalate alongside the years achieved in school. It is established into trigonometry, aiding students to solve non-right angle problems combining several mathematical methods. The pythagorean theorem assists many architects, engineers, and chemists in their respective careers....   [tags: Pierre de Fermat]
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Ockeghem: Missa Prolationum - Through the history of music, everything has changed drastically as the years pass. Music had a complete different structure in its early years to the one we know today. The writing was different, the language was different, the instruments were different, etc. Nevertheless, music has evolved through the different time periods to finally become what we know today. Each historical moment had different beliefs and of course that was reflected in the arts, the sciences and many other things. The Renaissance is a historical moment in which the influence of ancient cultures and therefore early philosophers as Pythagoras and Plato was very important; for that reason, the structure of music, as alm...   [tags: golden ratio, music history]
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How Much Deviation from Religious Doctrine is Acceptable? - Central to any religion is a unified set of beliefs that is shared amongst all its followers. These can range from stories about the origin of the universe or the lives of prophets or other important religious figures to sets of rules governing how you live your daily life. It is these beliefs that define who is a follower of that religion, and deviation from them could result in a person being outcast, persecuted, or even put to death in various areas and time periods. However, these beliefs are by no means universal....   [tags: Theology]
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From Divine Skepticism to Pleas for Divine Intervention - How much influence can a person have in the world before he or she turns thirty years old. Most people never have any true influence in the world and even fewer have done so while being in their twenties, but Christopher Marlowe, a 16th century English dramatist, is one of those few. Within his writings, Marlowe is able to steer his audience and keep them between blasphemy and heroism during a time when the known world executed those who did not believe in God. Marlowe steers his audience within this fine line in Doctor Faustus, a play in which the titular character views magic as a vehicle to gain wealth, power, and adoration....   [tags: doctor faustus, christopher marlowe]
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How Music Affects Test Scores in Mathematics K-6 - Most people have been introduced to the idea that music has a positive impact on the field of education, especially in mathematics. This has been a back-and-forth battle between advocates for music and the arts in schools and those looking for ways to deal with budget cuts. Logically thinking, music is based on math in that it deals with patterns and ratios (Vaughn, 2000). Research has shown that music, both music education and simply listening to music, can benefit students. The purpose of this study is to look at how music can affect test scores in the subject of mathematics in grades kindergarten through sixth grade....   [tags: connection between music and education] 2310 words
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The Development of Ancient Greece through Philosophic Evolution - ... On the establishment of the philosophic basis, one individual became a standard bearer of inquiry, who may still arguably be the predominate luminary of catechization, Socrates of Athens. Socrates found himself on a quest for understanding the moral rectitude in virtues such as courage and justice. As a result, Socrates was sincerely a good person who loved wisdom and the understanding that leads to it. He also appeared to believe that everyone carried an innate sense of goodness, which maintained credibility since the soul is pure....   [tags: philosophical analysis] 726 words
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“Writing to Learn” in a Math Classroom - Theory of “Write to Learn” Reading and writing are the basis of the original meaning of literacy. This definition, however, changed over time and culture. The term has expanded to include computer literacy, digital literacy, information literacy, health literacy, etc. (Vacca, Vacca, & Mraz, 2011). Nevertheless, the most important change to the term literacy is expanding the use of reading and writing. Literacy is defined as understanding, thinking and practicing the use of language in different cultural/social settings through the use of all types of media which allows people to communicate and make meanings (Vacca et al., 2011)....   [tags: Education, mathematics]
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It's Time to Move Beyond Equal Temperament - All these years, we have been brainwashed by hearing many classical and even rock pieces played on electric pianos. Music played on those instruments has made our ears become too dull to appreciate the true art. There is no need for that kind of equal temperament system of piano tuning anymore. Modern technology has developed to a point where one can simply press a button on an electric piano to change the key of any piece. The equal temperament today essentially limits an artist’s expression of different pieces to a universal standard....   [tags: Equal Temperament Music]
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Ancient Greek: The Birthplace of Western Civilization - ... Both the US and the Athenian government had the Legislative limb, the Executive extension, and the legal limb. The Legislative extension passes the laws, the Executive limb completes the laws, and the legal extensions had trials with paid members of the jury. In the US, a large portion of the just speculations that the administration utilization are either indistinguishable or fundamentally the same to the Ancient Athenians hypotheses. In reasoning old Greek kept tabs on the part of reason and request....   [tags: philosophy, fine art, socrates] 757 words
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The Classical World - The Classical World The Classical World made many contributions to the development of science, literature, and ethics. These contributions have influenced the modern world today. Many mathematicians, astronomers, and scientists contributed to the development of many of the luxuries we enjoy today. Homer, author of The Iliad and The Odyssey, made contributions to the field of literature through his writing. In the field of ethics, many philosophers from the Classical World contributed to the standards, values, and principles of our society today....   [tags: essays research papers] 551 words
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Musical Therapy: History and Medicine Impact - ... While these brave men rested in hospital wings, guess who came to visit them to help lift their spirits. A wonderful thing the most beautiful thing, music. Musicians of all sorts from all over would come and perform for the veterans, nurses and doctors said they noticed a reasonable change in the men, they became very sanguineness. This change in the residents gave the doctors an idea. Let’s hire musicians. This led to musicians being hired, ones with a required specific curriculum that was to be acquired through a program designed to fit the needs of everyone....   [tags: psychological analysis] 1337 words
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The Life of Nicholas Tesla - ... He then received a recommendation letter that was addressed to Thomas Edison, the “father of electricity”. Tesla and Edison worked together for a short amount of time before separating and becoming rivalries. Tesla worked to improve Edison’s power systems, such as the DC power station located in Manhattan with a plethora of sagging wires. Edison has promised Tesla $50,000 if he would better Edison’s systems; Edison fell through the promise which caused Tesla to quit. Since Tesla still had no money after working for Edison, he worked hard and found a company, specifically the Western Union Company, to invest in his AC motor....   [tags: engineer, physicist, visionary] 999 words
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The Beliefs of Plato vs Aristotle - When Socrates was sixty years old, Plato, then a youth of twenty, came to him as a pupil. When Plato was sixty years old, the seventeen-year-old Aristotle presented himself, joining the Teacher's group of "Friends," as the members of the Academy called themselves. Aristotle was a youth of gentle birth and breeding, his father occupying the position of physician to King Philip of Macedon. Possessed of a strong character, a penetrating intellect, apparent sincerity, but great personal ambition. Aristotle was a student in the Academy during the twenty years he remained in Athens....   [tags: Philosophy Philosophers Essays] 3776 words
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The Reality of Science - The Reality of Science Science is defined in the Merriam Webster dictionary as "an area of knowledge that is an object of study". What is the object of scientific study. Through an adherence to the rules prescribed by the scientific method, researchers and students of the various scientific fields search for truths, as defined by what can be proven to really exist; in short, they searching for what is real. It is the quest to define reality, for the purpose of mastering it; perhaps, to one day be able to manufacture reality in a vast warehouse in the likeness of the landscape-altering remnants that litter the hills and meadows of industrialized nations around the globe....   [tags: Psychology Essays] 1771 words
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The History of Physics - The History of Physics In order to attempt to trace the origins of the modern science that we now refer to as “physics,” we must begin with the origin of the term itself. Taken from the Greek word “physika” meaning growth or nature, physics most obviously began as the intelligent study of the human environment (Webster 393). From superstition and religious practices, the foundation of all other sciences was born. These concepts have subsequently grown into what we regard today as physics....   [tags: Papers] 1533 words
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Greek Contributions - Major Greek contributions include astronomy, optics, and acoustics, along with major advances in mathematics. Science in ancient Greece was based on logical thinking and mathematics. The Greeks were very interested to know about the world, the heavens, and themselves. Greek geniuses were articulate thinkers. (Pg. 55, Society and Technological Change) The Greek philosophers were very much drawn to mathematics. They invented its generality, analyzed its premises, and made notable discoveries of theorems by a rigid adherence to deductive reasoning....   [tags: Ancient History] 1476 words
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Mystery Cults - Mystery Cults Mystery cults greatly influenced the development of Pythagoreanism as Pythagoreans adopted many of their traditions, behaviors and beliefs. Pythagoras, the founder of the Pythagoreans, established a school in which he developed and taught these adopted cultural behaviors and beliefs. "The nature of daily living in the school, both its moral and its intellectual disciplines, can perhaps best be understood as an intellectualized development from earlier mystery cults such as the Eleusinian" (Wheelwright 201)....   [tags: Papers] 2592 words
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Euclid and the Birth of Euclidean Geometry - Euclid and the Birth of Euclidean Geometry The ancient Greeks have contributed much to the development of the Western World as we know it today. The Greeks questioned all and yearned for the answers to many of life’s questions. Their society revolved around learning, which allowed them to devote the majority of their time to enlightenment. In answering their questions, they developed systematic activities such as philosophy, psychology, astronomy, mathematics, and a great deal more. Socrates (469-399 BC) was an ancient Greek philosopher whose ideas mark the turning point in the history of knowledge and formal thought....   [tags: essays research papers] 901 words
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Contrasting The Religions of Christianity and Hinduism - The world has many different belief systems including Christianity and Buddhism. Both are similar and different in many ways. These religions are used in different places around the world and influenced the lives of its followers and the society in which they are practiced. Christianity is more diverse and complicated in its beliefs and totally depends on faith. In contrast, Hinduism is a belief more based on the simplicity of culture and tradition. Christianity was founded in the early first century....   [tags: religion] 677 words
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The History and Development of Music - As Plato said “Music is a moral law. It gives a soul to the universe, wings to the mind, flight to the imagination, a charm to sadness, and life to everything.” Music has a very complex history and it is used in a variety of ways. Music is used for entertainment and also in the medical field. Music has become an important part of the world since its birth, and its various uses around the world. Music became an important part of the world since its birth. Many people believe that music came about in The Renaissance, but in fact music history shows that music has been in this world since 500 B.C., the music came when Pythagoras experimented with the acoustics and how math related to the tones...   [tags: acoustics, emotion, style] 580 words
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Taking a Look at Dementia - ... The latter stated that the elderly were unsuited for any position of responsibility because "There is not much acumen of the mind that once carried them in their youth, those characteristics one would call judgement, imagination, power of reasoning, and memory. They see them gradually blunted by deterioration and can hardly fulfill their function." For comparison, the Roman statesman Cicero held a view much more in line with modern-day medical wisdom that loss of mental function was not inevitable in the elderly and "affected only those old men who were weak-willed"....   [tags: mental illnesses] 573 words
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The Use of Deception in William Shakespeare's Twelfth Night - The Use of Deception in William Shakespeare's Twelfth Night            Deception is a key theme in William Shakespeare's Twelfth Night. The characters must use deception to obtain good things, escape bad situations, or to play cruel hilarious ticks on other people. One example of deception is when Viola clothes herself in men's clothing in order to obtain a job under the Duke of Illyria, Orsino. During another scene Sir Andrew, Fabian, Maria, and Sir Toby Belch trick Malvolio into making a fool of himself....   [tags: William Shakespeare Twelfth Night Essays]
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The Important Role of Mathematicians in Society - The Important Role of Mathematicians in Society Thesis Statement This report will focus on the professional field of mathematicians. It will highlight some of the history, responsibilities, opportunities, and requirements of this occupation. Outline I. Introduction A. A condensed history of mathematics B. Famous mathematicians and their accomplishments II. Body A. Opportunities for mathematicians B. Education and training C. Requirements D. Earnings III. Conclusion A. Good mathematicians are problem solvers Mathematicians: Making numerous contributions A mathematician is described as someone who uses logic or theory to solve problems....   [tags: essays research papers fc]
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Expression of Renaissance Ideals throught the Art of the Period - Expression of Renaissance Ideals throught the Art of the Period The humanist and secularist beliefs of religion, individuality, and antiquity were evident in the style and illustration of Italian paintings and sculptures in the High Renaissance era. A deep sense of piety, Greek and Roman philosophy, and secularism, can be found in nearly all Renaissance paintings and sculptures, and the school of thought in Renaissance society that regarded the artist as genius contributed to all of these items....   [tags: European Europe History] 482 words
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Aristotle on Paideia of Principles - Aristotle on Paideia of Principles ABSTRACT: Aristotle maintains that paideia enables one to judge the method used by a given speaker without judging the conclusions drawn as well (I.1 De Partibus Animalium). He contends that this "paideia of principles" requires three things: seeing that principles are not derived from one another; seeing that there is nothing before them within reason; and, seeing that they are the source of much knowledge. In order to grasp these principles, one must respectively learn to recognize what distinguishes the subject matters studied in different disciplines, see first principles as coming from experience and acquire the habit of seeking them in one’s experien...   [tags: Philosophy Philosophical Essays]
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How Money Has Changed Society - How Money Has Changed Society *Works Cited Not Included Marshall McLuhan's lasting contribution is his vision of the ways technology affects and changes history and culture. McLuhan proposes that technologies are not mere add-ons to who and what humans are but, rather, alter them as though the technologies really are extensions of humans. Technology determines culture and history to the extent that it "shapes and controls the scale and form of human association and action." The introduction of money affected culture in that this new technology gave rise to accelerated change and growth within society....   [tags: Papers] 708 words
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Evolution of the Keyboard - The Physical Evolution of the Keyboard: From Monochord to Harpsichord Since the first person heard the wind whistle through the trees or the sea in a seashell humans have been drawn to sound. Being the oppressive and ingenious species that we are we felt the need to capture these sounds and any others that we could to keep for our own. Eventually people like Pythagoras and gods such as Apollo found that by stretching materials and picking/plucking them that they would produce sounds and that the tighter you stretched these strings the higher the sound would go....   [tags: essays research papers fc]
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The History of Math - The History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions....   [tags: Mathematics Education Logic Numbers Essays] 4777 words
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Analytical Response for Narrative of the Life of Frederick Douglas and Ralph Waldo Emerson’s Self Reliance - ... One of the authors is addressing a post slavery audience while the other is still fighting for the abolishment of slavery. Not only does this explain the differences in what they consider to be independence, but it also explains the different tones that each piece was written in. In Self-Reliance, Emerson delves into the notion that people are occupied with the need to please members of society. This will not help them reach their goal of self-reliance because they are fully dependent on getting the support from societies’ other members....   [tags: slavery, society, acceptance] 641 words
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How Would the World be Different if the Ancient Greeks had Decided Not to Colonize? - Early in the first millennium B.C.E., ancient Greece was reduced to ruins by bloodthirsty migrants who destroyed the educated class. Most of those who were fortunate enough to survive the devastation did so by goat farming (Fernandez-Armesto, 2011, p. 110). In order to escape their increasingly oppressive environment, the Greeks began to travel and explore far away from their homeland, colonizing areas along their routes and engaging in trade with other civilizations. As they continued to venture farther, they erected permanent dwellings, fabricated ornate shrines and created artistic masterpieces, some of which are still standing today....   [tags: Ancient Greece, Colonization]
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Music Therapy in Treating the Physiological or Psychological Aspect of an Illness or Disability - In the last decades of the information age, where technology has rapidly advanced and information is readily available through search engines connected to databases on the World Wide Web, medical studies have similarly advanced and enlarged their domain to psychological and physiological areas of study in addition to their traditional physical concerns. Music therapy, one area of study, has shown growing development and interest. Music therapist Deforia Lane defines music therapy as “the systematic application of music to aid in the treatment of the physiological or psychological aspect of an illness or disability” and notes that the human soul relates inseparably to this treatment (Lane 15)...   [tags: effective programs for healthcare]
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Analysis: The Explorer by Gwendolyn Brooks and Fredrick Douglass by Robert Hayden - The world we live is in no ways perfect. Our world is littered with pride and greed. We want money and to advance in our life and in some ways we forget the people we walk over. It is about the money and it doesn’t matter who gets in our way. Most people also have a problem with admitting their mistakes. The United States of America was at one time a country that on the outside seemed to be perfect, but in truth it had dark secrets. It held slaves for hundreds of years and once they were emancipated the world turned to other means....   [tags: freedom, hope and individuality]
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Investigating Ethical Issues from a Philosophical and Religious Perspective: Animal Experimentation - Hernandez 3 parts of an animal’s body, sometimes the entire body, to conduct experiments about stress. Other of the many destructive procedures include electrocution, tail suspension and drowning. (Office of Animal Care and Use, 2005) Not all of these animals die due to the causes of only one experiment however, these animals are kept in captivity and are continually tested on until they unfortunately meet their untimely deaths. It is due evidences such as these, that animal experimentation for medical research can be seen as productive for human or harmful to the lives of innocent animals....   [tags: animal abuse and testing]
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Looking through Life with an Invisible Hand in Adam Smith - ... Authors such as G.F Scarre and Helen Joyce also analyze the use of the "invisible hand", primarily focusing on its use for a well functioning society. Weakness: According to Smith's argument of a "invisible hand" society, it states that " each individual, in seeking her or his own gain , is led 'by an invisible hand' to promote the common good, through doing so is not her or his intention.( Philosophy 307)" What this is stating is a person should work hard for what they have earned and keep that revenue for themselves, not focusing on the benefits of others in society....   [tags: research paper proposal] 951 words
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Should Committed Environmentalists Choose to Adopt a Vegan/Vegetarian Diet? - Introduction The environmental impacts of a diet based in animal products is well documented and is the source of much debate. According to a controversial United Nations report entitled Livestock's Long Shadow (2006),“The livestock sector emerges as one of the top two or three most significant contributors to the most serious environmental problems, at every scale from local to global.” For those committed to reducing their environmental impacts, one solution would be to transfer to a vegetarian or even vegan diet....   [tags: Animal Rights ]
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