Pythagoras: a Universe Made of Numbers

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

4. Plato focuses on the ideas of piety and holiness, virtue and wisdom, laws and justice. In the Euthphyro he is

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 was born in 570 BCE. at Samos, Ionia, a city located in Greece . His mother being Pythais and his father is Mnesarchus. Not much was known about him because of the lack of written information on him. Pythagoras received a good education during his childhood, such as reciting homer, learning poetry, and playing musical instruments. Scholars come to believe that he got his astronomy from Anaximander and his mathematical/geometry knowledge from Miletos. Overall his mentor was Thales, he was the one to encourage Pythagoras to continue his studies and travel to Egypt. He developed a strong belief in numbers/mathematics, astronomy, and philosophy.

Plato’s moral theory consisted of the concept of the soul and the concept of virtue as function. To Plato, the soul has three parts; reason, spirit, and appetite. The reason we do things is to reach a goal or value, our spirit drives us to accomplish our goal, and our desire for things is our appetite. The three virtues that must be fulfilled to reach the fourth, general virtue are temperance, courage, and wisdom,

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

Many of the theorems we have today our proven fact, while back in Pythagoras’ day math was more critical thinking rather than problem solving. One example of Pythagoras’ critical thinking comes in the form of a simple triangle which he called Tetractys. A tetractys, or also known as tetrad, a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. This later became the mystic symbol of the Pythagoreans.

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.

For Pythagorean shapes and numbers was so important. He believed that the most perfect shape of the nature is circle. Therefore he put the earth in the center of a spherical world. According to Plato the movement of planets is in perfect circles. However now its known that the planetary orbits are ellipses and not

The author of Journey through Genius, William Dunham, begins this chapter by depicting how mathematics was spurred and developed in early civilizations. Dunham focuses primarily on the works’ and achievements’ of early Egypt, Mesopotamia, and Greece in this section. These ancient societies, as they developed, produced mathematicians such as; Thales, Pythagoras, and Hippocrates, who turned a basic human intuition for space and quantity into applicable everyday mathematics. The primary influences driving the development of early mathematics were the issues of growing civilizations, most notably counting commodities, taxation, and the division of land equally, rather than a pure desire for understanding that is seen in mathematics today. These influences culminated in the development of early arithmetic and geometry.

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

Ancient Greek mathematicians contributed enormously to fundamental math that built up from practical math such as geometry, engineering, astronomy and the astonishing academic contributions to worldly influences. Greek mathematicians would the one of the earliest civilizations to transform mathematics into rational thoughts when viewing all the concepts in the world. From ancient mathematicians such as the Egyptians and Babylonians, they both viewed their calculations through reasoning and using repeated observations to seek solutions to their equations. There was no real framework of their proof being certain since geometric considerations played a second role in arithmetic formulas. Greek mathematicians were influenced by the Egyptians and

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.