History of Geometry
The first mathematics can be traced to the ancient country of Babylon and to Egypt during the 3rd millennium BC. A number system with a base of 60 had developed in Babylon over time. Large numbers and fractions could be represented and formed the basis of advanced mathematical evolution. From at least 1700 BC, Pythagorean triples were studied. The study of linear and quadratic equations led to form of primitive numerical algebra. Meanwhile, similar figures, areas, and volumes were studied as well as the primitive values for pi obtained. The Greeks inherited the Babylonian principles and developed mathematics from 450 BC. They discovered that all real numbers could not accurately express all values, such as relationships between sides. Irrational numbers were born. The Greeks progressed rapidly in mathematics from 300 BC. Progress also sped in the Islamic countries of Syria, India, and Iran. Their work had a different focus from that of the Greeks, but all Greek principles held! true. This basis was later brought to Europe and developed further there. The Babylonian system of writing was called cuneiform and was based on a series of straight lined symbols. These symbols were wet and baked in the hot sun to preserve. Curved
lines could not be drawn. These cuneiform symbols led to many tables used to aid calculation. As stated previously, they used a base 60 system, which has ten proper divisors, instead of our current system, base 10 with only two proper divisors. In this respect, their system may have been more advanced since many more numbers have a finite form. Two examples of these tables are the tables found at Senkerah on the Euphrates River in 1854, which date from 2000 BC. This table was used to figure the squares of numbers to 59 and cubes of numbers up to 32. However, a drawback of this system is the lack of a proper 0. Also, context was required to determine if 1 meant 1, 61, or 361, etc. Pi has baffled and intrigued scientists and mathematicians for thousands of years. Perhaps they believe there is something about pi that would ease all other types of calculations. Perhaps they believe pi holds the key to future computation in areas of mathematics yet unexplored. Whatever it is, many more surprises and discoveries are to be made. Many say that the Babylonians first developed systems of quadratic equations. This calls for over simplification, because the Babylonians had no concept of an equation. Also, all solutions to Babylonian problems were positive because they were solutions to problems involving lengths. Euclid deduced many theorems and other conjectures from his five original postulates. Many porisms, now called corollaries, and many lemmas, or something assumed in the proof of a theorem, were used. Furthermore, many propositions in the later books were based on previous theorems proven true. In the theory of parallels we are even now not further than Euclid. This is a shameful part of mathematics... Also, in China in the fifth century, Tsu Chung-Chih calculate pi correctly to seven digits. Later in 1430, Al-Kashi of Samarkand computed pi to 14 places. Machin invented the formula The most important discovery of this school was the fact that the diagonal of a square is not a rational multiple of its side. This result showed the existence of irrational numbers. Not only did this disturb Greek mathematics but the Pythagoreans' own belief that whole numbers and their ratios could account for geometrical properties was challenged by their own results. It has been stated than Euclid was
Some common words found in the essay are:
Al-Kashi Samarkand, Girolamo Saccheri, BC Alexandria, Abu Abd-Allah, Samos Greek, Greeks Greek, BC Pythagorean, John Playfair, Euphrates River, Babylon Egypt, fifth postulate, straight line, + 1/5 *, proper divisors, book elements, tan^-1 *, believe pi, mathematics astronomy, 1/7 *, 300 bc, 1/5 *,
Approximate Word count = 1568
Approximate Pages = 6 (250 words per page double spaced)
|
