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Science & Information Technology => Science Discussion Forum => Topic started by: jas_fluidm on March 05, 2012, 03:45:29 PM
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Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic. The markings include six prime numbers (5, 7, 11, 13, 17, 19) in order, though this is probably coincidence.
The advanced artifacts of Egypt's Old Kingdom and the Indus-Harrapa civilization imply strong mathematical skill, but the first written evidence of advanced arithmetic dates from Sumeria, where 4500-year old clay tablets show multiplication and division problems; the first abacus may be about this old. By 3600 years ago, Mesopotamian tablets show tables of squares, cubes, reciprocals, and even logarithms, using a primitive place-value system (in base 60, not 10). Babylonians were familiar with the Pythagorean theorem, quadratic equations, even cubic equations (though they didn't have a general solution for these), and eventually even developed methods to estimate terms for compound interest.
Also at least 3600 years ago, the Egyptian scribe Ahmes produced a famous manuscript (now called the Rhind Papyrus), itself a copy of a late Middle Kingdom text. It showed simple algebra methods and included a table giving optimal expressions using Egyptian fractions. (Today, Egyptian fractions lead to challenging number theory problems with no practical applications, but they may have had practical value for the Egyptians. To divide 17 grain bushels among 21 workers, the equation 17/21 = 1/2 + 1/6 + 1/7 has practical value, especially when compared with the "greedy" decomposition 17/21 = 1/2 + 1/4 + 1/17 + 1/1428.)
While Egyptians may have had more advanced geometry, Babylon was much more advanced at arithmetic and algebra. This was probably due, at least in part, to their place-value system. But although their base-60 system survives (e.g. in the division of hours and degrees into minutes and seconds) the Babylonian notation, which used the equivalent of IIIIII XXXXXIIIIIII XXXXIII to denote 417+43/60, was unwieldy compared to the "ten digits of the Hindus."
The Egyptians used the approximation π ≈ (4/3)4 (derived from the idea that a circle of diameter 9 has about the same area as a square of side 8). Although the ancient Hindu mathematician Apastambha had achieved a good approximation for √2, and the ancient Babylonians an ever better √2, neither of these ancient cultures achieved a π approximation as good as Egypt's, or better than π ≈ 25/8, until the Alexandrian era.
reference: http://fabpedigree.com/james/mathmen.htm
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Very knowledgeable post for all...............................
thanks
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Thank you very much for this post. We (who work with mathematics) should share this type of post that increase our knowledge.
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Thanks
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Thanks for your post. It's knowledgeable.
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For the interested readers, who want to know more about the earliest history and historical development of egyptian, babylonian, mesopotamian, greek mathematics, I would like to recommend the following books of my collection.
Newman, J. R. The World of Mathematics Vol. 1-4, Simon & Schuster, 1956.
Boyer, C. B., Merzbach, U. T. A History of Mathematics, foreword by Isaac Asimov, 2nd ed. Wiley, 1991
Boyer, C. B., Merzbach, U. T. A History of Mathematics, foreword by Isaac Asimov, 3rd ed. Wiley, 2011
Cooke, R. The History of Mathematics A Brief Course, Wiley, 2005
Hodgkin, L. A History of Mathematics From Mesopotamia to Modernity, Oxford University Press, 2005.
Martzloff, J. C., Wilson, S. History of Chinese Mathematics, Springer, 2006
Gregersen, E. (ed.) The Britannica Guide to History of Mathematics, Britannica Education Publishing, 2011
Stillwell, J. Mathematics and Its History, 3rd ed. Springer, 2010.
Robson, E., Stedall, J. The Oxford Handbook of The History Of Mathematics, Oxford University Press, 2009.
Burton, D. The History of Mathematics An Introduction, McGraw-Hill, 2005.
Kleiner, I. Excursions in the History of Mathematics, Birkhäuser, 2012.
González-Velasco, E. A. Journey through Mathematics Creative Episodes in Its History, Springer, 2011.
Gow, J. A Short History of Greek Mathematics, Cambridge library collection, Cambridge University Press, first published in 1884, digital version printed in 2010.
Robson, E. Mathematics in Ancient Iraq A Social History, Princeton University Press, 2008.
Tabak, J. Mathematics and the Laws of Nature Developing the Language of Science The History of Mathematics, Revised ed. Facts on File, 2011.
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Beside the post 'Earliest mathematicians' Books references of Murad sir will make the readers more inquisitive about the history of early mathematics.