Pythagoras Research Paper

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

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.”

Among these people were Copernicus who believed the sun was at the center of the world and the earth, stars and planets revolved around it. Danish astronomer Brahe helped contribute to this idea by contributing a large mass of data about the universe that he was able to discover. His student Kepler kept his ideas going, as he formulated many laws of planetary motion. He said the orbits around the sun were elliptical, planets don’t move in a uniform speed and the time a planet completes its orbit is related to its distance from the sun. Meanwhile, Florentine Galileo decided to use experiments to find out what happened and not what should happen, and discovered that a uniform force makes a uniform acceleration as well as inertia laws, that an object will be in motion forever unless stopped by another force.

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.

a2+b2=c2 is the famous theorem that Pythagoras discovered and named, calling it the Pythagorean Theorem. This theorem applies to the right triangle stating, that by adding the length of both legs squared you can then find the squared length of the hypotenuse. This theorem is set up in way that if you know two of the variables, whether it is a leg(b or a) and the hypotenuse (c) or both legs (a and b), you will always be able to find the third measurement. However, why does this theorem work? Why does a2+b2=c2? That is the question that is asked hundreds of times by thousands of people. The answer to it is not a complicated one, the reasoning behind that is because there are at least 367 Pythagorean Theorem proofs out there (Source four). They

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.

A few things I found interesting when I watched “Donald In Mathmagic Land”, was an ancient Greek man named Pythagoras also known as the father of mathematics. He discovered many fundamental things such as fractions that helped him create a formula that soon became the basis to music with the help of his fraternity as well. A secret pentagram was used as a password entry to for their meetings in order for them to speak about their mathematical discoveries. I did not know that mathematics was essential in order to create music. Pythagoras also discovered the pentagram had many mathematical functions such as the golden section and many shapes. One of the shapes found within the pentagram was the golden rectangle which helped create famous sculptures,

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

Archimedes produced formulas to find the area of regular shapes by using the shapes he already knew how to calculate (The History of Archimedes). An example of this would be the circle. Archimedes would draw a polygon on the outside of the circle and then a smaller one on the inside and he would solve the area of the polygons. Although he knew this only would only get him a range and that the actual calculation might never be found (The History of Archimedes). He similarly was able to find the calculation of the volume of a sphere. He did this by cutting the sphere into a series of cylinders, (The History of Archimedes) and then adding the volumes of the cylinders. Archimedes noticed that the smaller he cut the cylinders the more accurate. His approximation eventually became an exact calculation. Despite all of Archimedes’ contributions to mathematics, the story he is probably the most well-known for would be his discovery of a method for finding the volume of an object with an irregular shape (The History of Archimedes). Hiero had asked the royal goldsmith to fashion a new royal crown for him. Hiero provided a thing of gold to make it, but once Hiero was given his newly made crown he began to believe that the goldsmith cheated him out of some of his gold a replaced it with silver. He asked Archimedes if he could determine this. So while bathing Archimedes noticed

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

     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.