A timeline and brief history of numeral systems were indicated from 4700 B.C. to 1500 A.D. Many cultures through-out the world had developed numeral systems for their own community technological advancement.
Mathematical games and recreations started around 1850 BC and continued on to the present by famous mathematicians. The biographies of mathematicians who invented the games are reported including pictures and graphs in this web site.
The magic square has been studied for a long period of time. It shows how a magic square is formed and who studied the magic squares.
Aristotle wrote a book called "TOPICS" which started out with a discussion of deductive logic. The whole world reestablished this book starting with the Islamic translation on through time.
The birth of Greek astronomy has been attributed to Thales of Miletus. Thales brought from Egypt a number of fundamental geometric principles. Thales, an Ionian (western border of Asia Minor) who was active near the start of the sixth century bc has been credited with a number of geometric theorems. 1. A Circle is bisected by its diameter. 2. Angles at the base of any isosceles triangle are equal. 3. If two straight lines intersect the opposite angles formed are equal. 4. If two triangles have two angles and one side respectively equal, the triangles are equal in all respects. Thales was also well known for forecasting the solar eclipse, so he was also considered a scientist.
It is believed that the Emperor Huang-ti (27th century bc) was the first patron of mathematics. The Chinese believed that numbers had philosophical and metaphysical properties. The Chinese used numbers "to achieve spiritual harmony with the cosmos." They believed man's "....existence depended upon numerically specified actions and obligations." Under Huang-ti's rule, his ministers, Tai-mao and Li-shou devised a sexigesimal based number system and corresponding arithmetic.
In 386 BC in Athen's Greece Plato's friends bought for him a local orchard in which he founded one of the world's first universities. It was destined to become the intellectual center of Greece for over nine hundred years. The academy was technically a religious fraternity. The students paid no fees but most came from rich families and were expected to donate. Women were also admitted to the student body as Plato was an ardent Feminist. The chief studies were mathematics and philosophy. Over the main entrance was the motto " Let no one without Geometry enter here" The main requirement for entrance was a passion for Geometry.
Most of the major mathematical advances of the 4th century were made by those who studied at the academy. Their mathematical courses included arith- metic, theory of numbers, advanced geometry and astronomy. Plato and his aides taught by lecturing, by dialogue and by setting problems for the students to solve. One such problem was to find " The uniform and ordered movements of which the apparent motions of the planets can be accounted for". Their lectures were very technical with very abstract philosophical leanings. Students then, as always complained that their studies were not relevent enough for every day life. Many great scholars were tremendously influenced, including Aristotle whose notes and papers are still being studied today.
The Babylonians had an advanced number system, in some ways more advanced than our present system. Their proof of evidences that found in clay tablets and papyrus are a positional system with base 60 rather than the base 10 of our present system, the pythagorean triples, and the volume formula of truncated pyramid.
This greek philosopher, Zeno, is duely noted for developing the paradox of infinity. His many paradoxes involve never ending motion of an object.
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