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.”
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.
This theorem is one of the key results in elementary geometry. Pythagoras honored the study of numbers more that anyone and made many advances in it. He transformed the philosophy of geometry and made it a form of open-minded education (Zhmund
Those discoveries influenced the ancient world as well as today. And, people continue to apply them today. In Mathematics, the Pythagorean believed that “numbers were like gods, pure and free from material change … They believed
Brumbaugh says that it hard for us today, familiar as we are with pure mathematical abstraction and with the mental act of generalization, to appreciate the originality of this Pythagorean contribution because we do not know in what sense Pythagorean and mathematikoi were studying mathematics. Regarding to this we do not know what work is his anf what is his followers because there wasn’t much writing.
When he was given freedom, he formed a school in Samos, called "The Semicircle," but soon left to travel to Italy. He traveled to southern Italy, to the town of Croton, where he founded a religion based school. He also developed a small group of his top followers called the Mathematikoi. In this school, Pythagoras made great discoveries. Some achievements of Pythagoras include, classifying numbers into even and odd, classifying perfect numbers, and classifying triangle numbers. His biggest discovery is most definitely the Pythagorean Theorem. This property's equation states that a^2+ b^2 = c^2, with the variables a, and b acting as the two legs of a right triangle, and c acting as the hypotenuse. The Pythagorean Theorem was the start of basic trigonometry, and geometry. When you hear the phrase Pythagorean Theorem, most people revert to saying that Pythagoras invented it. Well... no. Basically, Pythagoras heard the idea proposed in Babylon, so he stole it for himself and refined it a bit. Even so, the little bit of refining he did was something that the Persians probably couldn't have done. Pythagoras was proud of his achievement, but then one of his own students turned on
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
Pythagoras was one of many math Mathematicians and a Greek Philosopher . He was born 570 BCE Samos, Ionia and died 500-490 BCE Metapontum, Lucanium. He also was the first philosopher ever. Pythagoras came up with the Pythagorean Theorem. The Pythagorean Theorem is a among all 3 sides of the triangle. There's also a formula that goes along with Pythagorean Theorem, the formula is (a2 + b2 = c2). We still use Pythagorean Theorem til this day. That formula only applies to right triangles. The Pythagorean theorem has shocked people for nearly 4,000 years. There are now almost 367 different ways to do it. Pythagoras left Samos and went to Italy to continue with the Theorem. One of Pythagoras famous quotes was “As soon as laws are necessary for
It was Euclid’s Elements that inspired mathematicians to take it one step further and solve the things that Euclid had left out, such as squaring the circle with only a compass and a straightedge. The difficulty of these problems led mathematicians to change the way that they
Even though Pythagoras was a mathematical leader, but he is also a respected teacher of religion in ancient Greece because of his religious beliefs and those who followed him. By teaching self-discipline and dedication, embracing as it did a vast number of ancient beliefs, infusing music, math and cosmos, made him one of the greatest teachers, philosophers, and mathematicians in the world.
His work is the most pioneering in the fields of mathematics that established his legacy in geometry, calculus and trigonometry. Leonard Euler’s work is responsible for the development of modern mathematics through the application of his concepts.
In the beginning there was Euclid. The geometry we studied in high school was based on the writings of Euclid and rightly called Euclidean geometry. Euclidean geometry is based on basic truths, axioms or postulates that are “obvious”. Born in about 300 BC Euclid of Alexandria a Greek mathematician and teacher wrote Elements. The book is one of the most influential and most published books of all time. In his book the Elements Euclid included five axioms that he deduced and which became the basis for the geometry we now call Euclidean geometry. In Greek Euclid is Εὐκλείδης which means “renowned, glorious”. This fits his work for he has been called the “father of geometry” and his works continue to influence mathematical fields today. Elements was first set in type in 1482 in Venice making it one of the earliest mathematical books to be printed following the invention of the printing press. It is estimated by Carl Benjamin Boyer to be second only to the Bible in the number of editions published, with the number reaching well over one thousand. For centuries the quadrivium was included in the curriculum of all university students and knowledge of at least part of Euclid 's Elements was required of all students. When the content became part of other textbooks, during the 20th century, it ceased to be considered something all educated people had to read.