How Did Pythagoras Contribute To Geometry

The creations of Pythagoras were very powerful during the era in which he lived in. He created a community of followers (known as the Pythagoreans) who believed that mathematics was fundamental and ‘at the heart of reality’ (source 1). The people in the society were all proficient mathematicians took mathematics very seriously, to the extent that it was similar to a religion (source 1).

Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which relates the two sides of a triangle to the hypotenuse using the formula a squared plus b squared equals c squared. However, because legend and obfuscation cloud his work even more than that of other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were

The Pythagorean School, for example, contributed many ideas to the mathematic community, among them, studies of geometry and the theory of proof.5 Euclid also lived in the time of ancient Greece and became a prominent mathematician, as well as author of a book about geometry called, The Elements, considered the second best-selling book of all time.6 The works of Pythagoras and Euclid have become fundamental building blocks for any person with an eighth-grade understanding mathematics. With these advancements, as well as innovations from Archimedes and Apollonius of Perga, Islamic scholars translated their works and contributed even more, growing the worldwide understanding of mathematics.7 Greek progressions in geometry as well as the theory of proof contributed greatly to our ultimate understanding of contemporary mathematics, without which, our modern society would be

Pythagoras also contributed to the music world. He expressed the musical harmony in formulas. He created a scale layout with gongs in different sizes and he proved that in the resonance of the gongs he hit, 1 octave interval is equal to 2:1 proportion, the perfect fifth is equal to 3:2 proportion, perfect four is equal to 4:3 proportion and whole notes are equal to 9:8. This, later started to be known as “Pythagorean Tuning.”

Hipparchus was a greek astronomer, geographer, and mathematician born 190 B.C. in Nicaea and died in 120 B.C. Rhodes, Rhodes, Greece. Hipparchus is accredited as the inventor of trigonometry because of his discovery of the first table of chords and also because he's the only person with valid data of the discovery and usage of trigonometry. In order to calculate the rising and setting of zodiacal signs, Hipparchus brought to light the division of circles into 360 degrees and the calculation of chords by looking at the triangles (spherical triangles or triangles that made up a circle) differently. Hipparchus experimented putting all triangles to be within a circle and with the three points each touching the

One of Thales’ most renounced findings include his discovery in geometric studies in the area reading the rules of triangles. He came to the conclusion that if the base angles of an isosceles triangle are equal, the sum of the angles of a triangle are equivalent to two right angles. With the application of “geometric principles to life situations, Thales was able to calculate the height of a pyramid by measuring its shadow, and the distance of a boat to the shore, by using the concept of similar triangles” (pg. 5, Muehlbauer). Realizations such as these helped shape the beginning for the formation of natural law based on observations of the world through explanation.

Speaking of triangle’s Pythagoras’ most famous contribution to the world of mathematics, The Pythagorean Theorem was proved during this time period. Pythagoras did not create the Theorem, the creation is credited to the Babylonians and Indians, however Pythagoras was the first man to successfully prove the Theorem. The iconic equation looks like

The Greeks made several inventions, most notably in the subject of math, which are still studied today and taught in school. Mathematician Euclid is often credited as the “Father of Geometry” for all his work and studies in this subject, which are compiled in his books called The Elements. He organized known geometrical statements called theorems and logically proved all of them. He proved the theorem of Pythagoras (another Greek mathematician), which stated that the equation (c2 = a2 + b2) is true for every right triangle.

The discovery of non-Euclidean geometry is credited to nineteenth-century mathematicians Carl Friedrich Gauss, Nikolai Ivanovich Lobachevsky, and János Bolyai because they are first to recognize that the negation of Euclid’s Fifth Postulate as an axiom produced another geometry that was as rich and solid as that of Euclidean geometry (Venema, 2012). However, several concepts of Hyperbolic geometry were already known by that time, it just was not labeled as Hyperbolic geometry (or non-Euclidean geometry) because Hyperbolic geometry was not yet “discovered”. Euclid’s work was so distinguished that it was accepted as the standard so people did not think it was possible for other geometries to exist. All in all, the discovery and growth of Hyperbolic geometry first began with several mathematicians trying to prove that Euclid’s Fifth Postulate could be eliminated as an axiom.

Pythagoras was an Ionian Greek philosopher, mathematician, and the founder of pythagoreanism, he is also often referred to as the first pure mathematician. The Pythagoreans advance the mathematics and showed that is needed in our everyday life. Pythagoras was well educated, and he played the lyre throughout his lifetime, and also knew poetry. He was interested in mathematics, philosophy, astronomy and music, and was actually greatly captivated by Pherecydes (philosophy), Thales (mathematics and astronomy) and Anaximander (philosophy, geometry). Pythagoras stayed in Crotona, a Greek colony in southern Italy, where he found a school where most of his followers lived. He was the master of society and all his followers were known as mathematikoi

In Famous scientist’s (2015) article Pythagoras it states that five 3D solids were brought into existence by Pythagoras and the Pythagoreans, these items are identical on all of the sides and today they are called dice. The ranged from four sides all the way up to twenty and later Plato believed they belonged to the five Greek elements including aether (n.pag). They said “Pythagoras believed that, like everything else, music was based on whole number ratios. He also believed in its healing properties.”(n.pag) He later would learn that music was controlled by rations, like if a sting is shortened by half it raises an octave or if it’s shortened two-thirds then it moved the pit up one-fifth discovering that octaves are split into fifths not halves (n.pag). Those are the biggest discoveries of Pythagoras and the Pythagoreans, but they still has many more different discoveries. He has been accredited with a lot for being an enigma, and having written no books in his life. Even so the thoughts from learning of this brilliant mathematician tickles the mind and creates great and wonderful thoughts and ideas for many people. Learning about all of this should inspire anyone to travel and learn the ways of other countries and customs and even grasp their mathematical

Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall, 150. ISBN 0-02-318285-7. “Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (ca. 287–212 B.C.), the most original and profound mathematician of antiquity.”

Eratosthenes was a great Ancient Greek mathematician known for creating the Sieve of Eratosthenes. He is also known for measuring the circumference of the earth accurately. He was born in Cyrene, Greece, which is now known as Libya, North Africa, in 276 B.C. He was born to Agalus and his wife. After his birth he was at the front seat of learning, he was educated at The Plato’s Academy in which he learned under the philosophies of Plato.

     Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know

Euclid Of Alexandria may be the best-known mathematician of the world, he is best known for his work on mathematics The Elements. The fact that his work has survived so long, 2000 years in fact, is a tribute to his mathematical genius, however very little of him is known. Three theories abound as to the true nature of this historical figure. Not all historians agree that Euclid was in fact a historical figure, some argue that the school in Alexandria took up the name Euclid to publish their works. But the more accepted theories are that Euclid was in fact a real historical figure who may have been the leader of a team of mathematicians.