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All of what we know of Pythagoras and his followers come from commentators who lived a hundred years of more later, since it appears that all knowledge and information was passed on orally. This empire lasted for over two centuries until it was divided by the successors of Alexander the Great. Four of the paradoxes were to have a significant impact on the development of mathematics. E) Under the leadership of the statesman Pericles, Greece reached the height of its glory in the 5th century BCE.What has become evident is that Pythagoras and his followers were considered to be, among other things, pure mathematicians. An interesting discussion of these can be found at Hippocrates of Chios (470 – 410 B. E.) Hippocrates of Chios was an excellent geometer who taught in Athens. Pericles was born to a family of wealth and position.

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THE PLAGUE IN ATHENS DURING THE PELOPONNESIAN WAR The plague in Athens was caused by the war strategy of Pericles. The curve may be used for dividing an angle into any number of equal parts.

His strategy was to bring all citizens from the surrounding area into Athens and let the Spartans have control of the outlying area. It appears that this was the first curve in in mathematics that was not either a straight line or part of a circle.

The site was first prepared by leveling the surface and then blocks of stone were transported and placed.

It was finished with an outer casing which was used to smooth the surface. Some interesting data: it is 756 feet long on each side, 480 feet high and is composed of approximately 2,300,000 blocks of stone, each averaging 2 1/2 tons in weight. This is a positional number system based on sixty, rather than ten.

Much of the early Greek arithmetic and geometry can be traced back to the Pythagoreans. He worked on the problems of squaring the circle and duplicating the cube. Among his accomplishments was to bring the ordinary citizen into the Athenian democracy.

While working on the problem of squaring the circle, he was able to find the areas of lunes. E.) Hippocrates of Cos is known to us as the Father of Western Medicine and he is credited with originating the Hippocratic Oath that all doctors take upon completing their studies. He was a gifted orator as was documented by the historian Thycidides.(Legend has it that this Minoan civilization is the lost civilization of Atlantis! E.) Thales seems to be the first known Greek mathematician and philosopher. Pythagoras founded a philosophical and religious school in Croton (now Crotone, in southern Italy) that had many followers.) The Founding of Rome is very much embroiled in the myth involving Romulus and Remus and Aeneas. This date has been traditionally celebrated in Rome with the festival of Parilia. He is often referred to as one of the Seven Sages of antiquity. (Pythagoras had started an earlier school in Samos which he abandoned.) Pythagoras was the leader of a Society (Brotherhood) which included an inner circle of followers known as mathematikoi.For about 4500 years it was the tallest building in the world. There is much speculation on exactly how this pyramid and its companions were actually constructed. They used a vertical wedge to represent a unit and a sidewys wedge to represent ten units.With arrangements of these two symbols they could represnt numbers of any size.The angles between two intersecting straight lines are equal. All knowledge and discoveries were attributed to Pythagoras. E.), the Persians, under the leadership of King Cyrus, took Babylon, the ancient capital of a middle eastern empire covering modern Iraq, Syria, Lebanon, and Israel, and thus became masters of Western Asia. E.) Parmenides was Greek philosopher who was a follower of Pythagoras. Philosophers of his time considered his philosophy to be quite negative.

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