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.…
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.…
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.…
The ancient Greek mathematician Euclid influenced mathematics in a large way after developing the Pythagorean theorem. His theorem (written around 300 B.C.) stated that “If two straight lines cut one another, the vertical, or opposite, angles shall be the same” (Doc. 5). Euclid wrote this theorem to set a base rule to help find the sum of the angles of a triangle. The Pythagorean theorem is still used today in mathematics thanks to Euclid’s contribution to society.…
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.…
Archimedes is universally acknowledged to be the greatest of ancient mathematicians. He studied at Euclid's school (probably after Euclid's death), but his work far surpassed the works of Euclid. His achievements are particularly impressive given the lack of good mathematical notation in his day. His proofs are noted not only for brilliance but for unequalled clarity, with a modern biographer (Heath) describing Archimedes' treatises as "without exception monuments of mathematical exposition. Archimedes made advances in number theory, algebra, and analysis, but is most renowned for his many theorems of plane and solid geometry. He was first to prove Heron's formula for the area of a triangle.…
Pythagoreans have and will continue to give recognition to Pythagoras for 1) the angles of a triangle equaling to two right angles. 2) The Pythagoras theorem, which is a right-angled triangle, and the square on the hypotenuse equaling to the sum of the squares on the other two sides. This theory was created and understood years earlier by the Babylonians, however, Pythagoras proved it to be correct. 3) Pythagoras constructed three of the five regular solids. The regular solids are called tetrahedron, cube, octahedron, icosahedron, and dodecahedron. 4) Proving and teaching that the “earth is a sphere in the center of the universe and that the planets, stars, and the universe were spherical because the sphere was the most perfect solid figure numbers. He also taught that the paths of the planets were circular (Douglass, 2005).” Pythagoras was also the first known person to recognize that the morning star and the evening star were in fact the same; planet Venus.…
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…
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.…
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…
Pythagoras was born in 570 BCE in Samon, Ionia, and died 500-490 BCE. He was a Greek mathematician and philosopher who is greatly known for his creation of the Pythagorean theorem. His principles influenced the work of Aristotle and Plato. Pythagoras migrated to…
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:…