Pythagoras made an experiment with strings by putting strings of the same length to the same tension and listening to the different sounds depending on where the strings would be divided. Pythagoras then proved that math and musical harmony are intertwined by describing the different results into intervals.…
There are many applications for the Pythagorean Theorem. For example, it can be used to find the distance between two cities given a reference city, the length of an edge in a right triangle if you are building a house, the magnitude of the velocity of a projectile given its horizontal and vertical speeds, and to find real power versus complex power for electronic utility companies.…
The Pythagorean theorem is one of the earliest theorems known to ancient civilization. The well-known theorem is named after the Greek mathematician and philosopher, Pythagoras. In the Wizard of Oz, after the Scarecrow gets a brain, he states the Pythagorean theorem. However, he mistakenly says it applies to an isosceles triangle when it applies to a right triangle. He not only says the wrong triangle, he also gets the equation wrong.…
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.…
At one point, the Greeks strongly believed that the numeral one was a unit not a number. Mathematics has evolved on a large scale to suit our lives today. Mathematics has also branched out to different sub-sections such as calculus, geometry, trigonometry and algebra. Who was Pythagoras?…
Pythagoras considered himself a philosopher, not a mathematician, for which he is widely known. His teachings taught of a belief in a cycle of rebirth. He believed that souls could be reborn into animals, but no signs have pointed to a belief that humans could be reborn into plants. To escape this cycle, one was encouraged to live to high moral standards. For as much as he claimed himself a philosopher though, he largely based the life of his followers around mathematics. Followers of his swore oaths based on the sum of ( 1+2+3+4) . He is remembered most nowadays for the Pythagorean Theorem, the idea that the square…
A Greek Astronomer by the name of Hipparchus compiled the trigonometric table which measured the length of the chord subtending the various angles in a circle of a fixed radius r. In other words, Hipparchus made the first piece of the puzzle for the Unit Circle. His table was done in increasing degrees of 71.…
(ln ln x), invented the totient function and used it to generalize Fermat's Little Theorem, found both the largest then-known prime and the largest then-known perfect number, proved e to be irrational, proved that all even perfect numbers must have the Mersenne number form that Euclid had discovered 2000 years earlier, and much more. Euler was also first to prove several interesting theorems of geometry, including facts about the 9-point Feuerbach circle; relationships among a triangle's altitudes, medians, and circumscribing and inscribing circles; and an expression for a tetrahedron's area in terms of its sides. Euler was first to explore topology, proving theorems about the Euler characteristic, and the famous Euler's Polyhedral Theorem, F+V = E+2 (although it may have been discovered by Déscartes and first proved rigorously by Jordan). Although noted as the first great "pure mathematician," Euler engineered a system of pumps, wrote on philosophy, and made important contributions to music theory, acoustics, optics, celestial motions and mechanics. He extended Newton's Laws of Motion to rotating rigid bodies; and developed the Euler-Bernoulli beam equation. On a lighter note, Euler constructed a particularly "magical" magic…
For Pythagoreans, the principle of being is seen in what gives form and shape rather than what is formed and shaped. According to Pythagoras, number or mathematical principle was that which gives order, harmony, rhythm, and beauty to the world. This harmony keeps a balance both in the cosmos and in the soul. The mathematical order in beings is perceivable not by the physical senses but by senses of the soul. Pythagoras conceived mathematics as the method for liberating the soul from the bondages of bodily senses and essentially as religious training. For Pythagoras, the soul is immortal and the cultivation of the soul is achieved by the studies of truth and the ascetic life. Pythagoras was the first person who took up the issue of virtue in philosophy. Pythagoras argued that there are three kinds of men who came to the Olympic Games, just as there are three classes of strangers. The lowest consists of those who come to buy and sell, and next above them are those who come to compete. Best of all are those who simply come to look on. Men may be classified accordingly as lovers of gain, lovers of honor, and lovers of wisdom. That seems to suggest the doctrine of the tripartite soul, attributed to the doctrine of Plato. Pythagoreans also believed in the transmigration of the human soul after death into other animal forms. The doctrine…
Greeks such as Socrates, Plato, and Aristotle created mathematics and geometry. These discoveries are incorporated in almost everything we use today for example, how something is made or how we cook.…
Pythagoras of Samos, or simply Pythagoras is an iconic Greek philosopher and Mathematician, who is mostly known as the founder of the Pythogoreansim movement. Pythagoras was raised in the island of Samos located off the coast of turkey but later had moved to Croton, a city in southern Italy, where he accomplished most of his philosophical work. Pythagoras was a man of many interests, he enjoyed mathematics, philosophy, astronomy, and music. And while today he is known as a mathematician, in his own day he was known as (Stanford Encyclopedia of Philosophy, 2005).…
Later came the Pythagoreans who followed Pythagoras, the Father of Numbers. He said that the basis for everything was numbers. His idea was that everything could be broken down into numbers. If a volcano were to explode or a fire was to destroy a town Pythagoras believed that it was because of numbers. His idea is still being used today by scientists, mathematicians, and even higher level algebra students as he later created the Pythagoras theorem.…
Math and music are connected in many ways. Math is seen to be as very precise. Music is often seen as a way to express emotion. They are actually both very closely related together. Music is an expression of scales and notes that are strung together to make sound. Math is the subject of numbers and symbols used to write formulas and equations. At its foundation, music and math are related. In this essay, you will show that math and music are related in many ways. They are more closely related then what they are seen to be. Numbers to beats. Pitch to rhythm.…
due to how early of a record it is. Some believe this information to be accurate…
8. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. For example, if two sides of a right triangle have lengths 3 and 4, then the hypotenuse must have a length of 5. The integers 3, 4, and 5 together form a Pythagorean triple. There is an infinite number of such triples. Given two positive integers, m and n, where m > n, a Pythagorean triple can be generated by the following formulas:…