Mathematic Contributions of Greece

Mathematic Contributions of Greece:

Euclid:

The famous Greek mathematician Euclid (300 BC) is best known as the author of the Elements, the oldest book consisting of geometrical theorems, which is why many consider Euclid to be the “father of geometry.”

Historical Introduction:

Not much is known about Euclid personally. There have been speculations whether he was a creative mathematician himself or merely collected the work of others. Much data about Euclid is recounted by Proclus, a 5th-century-AD philosopher. Euclid and Archimedes are often considered contemporaries. Euclid’s mathematical education is thought to be obtained from Plato’s pupils in Athens.

No work about geometrical theorems older than the Elements of Euclid has survived. The Elements superseded all earlier writings. This made it hard for historians to find out the earlier mathematicians whose works were could have been more significant in the development of Greek mathematics than Euclid’s. The Greek mathematician Thales is known to have discovered a number of theorems in 600 B.C. that appear in the Elements.

Eudoxus was given credit for the discovery of the method of exhaustion. Book XII of the Elements uses this method. While earlier mathematics may have been initiated by concrete problems, for instance finding out areas and volumes, by the time of Euclid mathematics had grown into an abstract construction, an intellectual occupation for philosophers as compared to scientists.

Other Contributions and Accomplishments:

Majority of the work of Euclid is known only through references by other writers. The Data is on plane geometry. The word “data” implies “things given”. The treatise consists of 94 propositions related to the kind of problem where certain data is presented about a figure and from which other data can be deduced. For instance, if a triangle has one angle given, the rectangle contained by the sides including the angle has to the area of the triangle a given ratio.

The Latin and Arabic manuscript translations of the Elements were also done, but it was not until the first printed edition, published in Venice in 1482. The work was very influential in Western education. The first comprehensive English translation was made in 1570. The most important mathematical period in England, around 1700, Greek mathematics was examined most passionately. Euclid was widely respected by all major mathematicians, including Isaac Newton.

The developing prepotency of the sciences and mathematics in the 18th and 19th centuries earned Euclid a crucial place in the curriculum of schools and universities throughout the Western world. The Elements was considered educational as a primer in logic

Pythagoras:

Pythagoras, a very famous mathematician from Greece, as well as a religious teacher, was born in c. 575 B.C on the Samos Island. He was the leader of the school of thought that believed that souls could be transmigrated and also developed it as a universal principle.

His father was Mnesarchus. He ran to the South of Italy to get away from the oppression of the Polycrates who had come into power in 538 B.C. It is said that he has also been to Babylon and Egypt. He and his supporters came into power in the south of Italy in Croton. That’s where Pythagoras established a school for new sect. It is predicted that Pythagoreans participated in the home government so that they could preach people to lead pure and simple lives as per their teachings. But, unfortunately the enemies attacked the Pythagoreans and the whole sect was eradicated. So the Pythagoreans were either evicted from Italy or they left the town willingly after they were attacked. He passed away in c. 495 B.C. in Metapontum.

Mathematical Teachings

The parts between the Unlimited and the Limited were set by the Pythagoreans. It is assumed that Pythagoras himself that the universal principle was a number and limited and gave shape to matter. It was his research on the musical intervals that led to discover that the main intervals, that fell amid the initial four integers, could also be expressed in the form of numerical ratio. He also came up with a theory that the summation of the initial four integers is 10 and gripped the complete nature of the number.

Pythagoreans’ work regarding the “Tetractys of the Decad” was so respected that people preferred to oath by this rather than their gods. The famous theorem of the right angled triangles that was discovered by Pythagoras has already been found in the scripts from the time of Hammurabi, a king of Babylon. Still, Pythagoras did some remarkable work in arranging and organizing the knowledge of mathematics.

Pythagoras concluded the two contradictions, unlimited and limited, as vital principles. The evenness or oddness of Numerical is equated with Unlimited and Limited, just as plurality and one, female and male, left and right, movement and motionlessness, crooked and straight, darkness and light, oblong and square, and bad and good. It was not clear whether there were one or more reasons for setting out these categories.