- Essay About Great Greek Mathematician Pythagoras
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- Biography of Pythagoras Essay
- Geometry in Art & Architecture Unit 3
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Essay About Great Greek Mathematician Pythagoras
Get your paper now. Professional writers and researchers. Sources and citation are provided. This essay has been submitted by a student. This is not an example of the work written by professional essay writers. What is pythagorean theorem? So the Pythagoreans in their love of numbers built up this elaborate number lore, but it may be that the numbers that impressed them most were those found in the musical ratios.
The upper left frame shows Lubal or Jubal , from the Old Testament, "father of all who play the lyre and the pipe" and 6 guys whacking on an anvil with hammers numbered 4, 6, 8, 9, 12, The frames in the upper right and lower left show Pithagoras hitting bells, plucking strings under different tensions, tapping glasses filled to different lengths with water, all marked 4, 6, 8, 9, 12, In each frame he sounds the ones marked 8 and 16, an interval of called the octave , or diapason.
In the lower right, he and Philolaos, another Pythagorean, blow pipes of lengths 8 and 16, again giving the octave, but Pythagoras holds pipes 9 and 12, giving the ratio , called the fourth or diatesseron while Philolaos holds 4 and 6, giving the ratio , called the fifth or diapente.
These were the only intervals considered harmonious by the Greeks. The Pythagoreans supposedly found them by experimenting with a single string with a moveable bridge, and found these pleasant intervals could be expressed as the ratio of whole numbers. Raphael's School of Athens shows Pythagoras is explaining the musical ratios to a pupil. Under the tablet is a triangular number 10 called the sacred tetractys , that we mentioned earlier. This diagram from a book written in shows the famous Renaissance musical theorist Franchino Gafurio with three organ pipes and 3 strings marked 3 , 4, 6.
This indicates the octave, 3 : 6 divided by the harmonic mean 4, into the fourth, 3 : 4, and the fifth, 4 : 6 or 2 : 3. The banner reads, "Harmonia est discordia concors" or Harmony is discordant concord , propounding the thesis that harmony results from two unequal intervals drawn from dissimilar proportions.
The diagram shows compasses, suggesting a link between geometry and music. So after experimenting with plucked strings the Pythagoreans discovered that the intervals that pleased people's ears were. Now bear in mind that we're dealing with people that were so nuts about numbers that they made up little stories about them and arranged pebbles to make little pictures of them. Then they discovered that all the musical intervals they felt was beautiful, these five sets of ratios, were all contained in the simple numbers.
They must have felt they had discovered some basic laws of the universe.
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Quoting Aristotle again It seemed clear to the Pythagoreans that the distances between the planets would have the same ratios as produced harmonious sounds in a plucked string. To them, the solar system consisted of ten spheres revolving in circles about a central fire, each sphere giving off a sound the way a projectile makes a sound as it swished through the air; the closer spheres gave lower tones while the farther moved faster and gave higher pitched sounds. All combined into a beautiful harmony, the music of the spheres. This idea was picked up by Plato, who in his Republic says of the cosmos; ".
Upon each of its circles stood a siren who was carried round with its movements, uttering the concords of a single scale," and who, in his Timaeus , describes the circles of heaven subdivided according to the musical ratios. Kepler, 20 centuries later, wrote in his Harmonice Munde says that he wishes "to erect the magnificent edifice of the harmonic system of the musical scale. And later, "I grant you that no sounds are given forth, but I affirm. What does this have to do with art or architecture?
The idea that the same ratios that are pleasing to the ear would also be pleasing to the eye appears in the writings of Plato, Plotinus, St. Augustine, and St.
Biography of Pythagoras Essay
But the most direct statement comes from the renaissance architect Leone Battista Alberti , "[I am] convinced of the truth of Pythagoras' saying, that Nature is sure to act consistently. I conclude that the same numbers by means of which the agreement of sounds affect our ears with delight are the very same which please our eyes and our minds.
Alberti then gives a list of ratios permissible, which include those found by Pythagoras. We'll encounter Alberti again for he is a central figure in the development of perspective in painting. We'll also discuss another architect who used musical ratios, Andrea Palladio , who designed the Villa Capra Rotunda shown here.
I always wanted to make a pilgrimage to Crotone, site of the Pythagorean cult, but this is all that's there to mark their presence. Pythagoras and his followers died when their meetinghouse was torched. We'll have more on the Pythagoreans later, in particular their fondness for the star pentagram. Reading Newman, p. The History of Philosophy c. History of Art. 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, 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 Free Essays words 1. 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.
Better Essays words 4. 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.
Geometry in Art & Architecture Unit 3
Pythagoras felt that all things could be explained and represented by mathematical formulae. Powerful Essays words 4. Pythagoras made proofs to prove that is theorem is always correct and goes to all right-angled triangles Better Essays words 3 pages Preview. 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 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 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. He influenced Plato and Aristotle and made contributions to the development of mathematics and western philosophy Strong Essays words 4. 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.
Good Essays words 1. He was born around B. 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 Free Essays words 1 pages Preview.
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. Free Essays words 4 pages Preview. Free Essays words 4. It can however, work with an even number. Free Essays words 2. Pythagoras was a Greek mathematician. Pythagoras lived on the island of Samos and was born around BC.
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. 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 Free Essays words 9. 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 Task 1: a The numbers 5, 12, 13 satisfy the condition. Free Essays words 3. 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.
Free Essays words 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 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.