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Essay / Research Paper Abstract
5 pages in length. In this paper the
history of Algebra is presented and the role that it plays in
mathematics today. There is also discussion on some of the
mathematicians who played a key role in the advancement of
Algebra as well as examples of applications in which Algebra is
used. Bibliography lists 5 sources.
Page Count:
5 pages (~225 words per page)
File: D0_JGAalgbr.doc
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Unformatted sample text from the term paper:
who played a key role in the advancement of Algebra as well as examples of applications in which Algebra is used. THE HISTORY OF ALGEBRA The first work
written concerning algebra was written by Diophantus of Alexandria in the 3rd century AD. Algebra is from the Arabic al-jabr or literally "the reunion of broken parts." The
word also means the surgical treatment of fractures. Algebra began to see more widespread use through the title of a book ilm al-jabr wal-mukabala "the science of restoring what
is missing and equating like with like" (PG). This was written by the mathematician Abu Jafar Muhammad (active c.800-847). He introduced the writing down of calculations in place
of using an abacus ("History of Algebra" PG). In the very beginning, the simple terms used by the Babylonian sexagesimal system is base 60 with only two digits.
As authors Bashmakova and Smirnova explain in their book, The Beginnings and Evolution of Algebra, there were naturally weaknesses in this system with such few symbols. There was no
zero and, though the system is positional, the representations are not unique. However, it is necessary to understand the still amazing achievements of the Babylonians for this simplicity.
One should bear in mind that they could solve, for example, quadratic equations, and find Pythagorean triples and Babylonian triples (solutions to x2 + y2 = 2z2). Additionally, they
knew that "the sum of two squares times the sum of two squares is again the sum of two squares, the essential lemma for the proof of the two squares
theorem in number theory" (PG). This they knew around 4000 years ago (Bashmakova and Smirnova PG). The Babylonians, however, "only dealt with tables and with specific problems" (PG).
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