history-page4 - Two number systems Multiplicative Grouping...

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Indus Valley Modern day Pakistan Aryans settled in about 1500 BC (supplanting previous civilization in place for a millennium). Sanskrit Brahmi numerals for 1 through 9 date to about 300 BC Evolved into ours through time. Adopted by Arab/Islamic Mathematicians Introduced to west in Iberia and in studying Arab Mathematicians Won us over by 1500 AD But they used in cipher system Place-value Sometime in the next 1000 years. Yellow River Xia dynasty started about 2100 BC Like India, ancient Chinese math seems to have little intermixing, unlike other Eastern hemi- sphere civilizations. Almost totally independent until 400 BC. Principally indigenous until 17th century. Written math dates to 1300 BC. (Late Shang dynasty)
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Unformatted text preview: Two number systems Multiplicative Grouping (Shang and later) Symbols for 1-9 (1-3 are easy) and powers of 10 Communicate same as place-value more explicitly but less eFciently. Counting-rod numerals (Han, 100 BC) Looks like ... Dierent for odd or even place Greek Sparta settled in 1200 BC Two number systems Attic 500 BC Acrophonic (used rst letters of corresponding words) Additive like Hieroglyphic and Roman Ionian Traced back to 450 BC, won out about 300 BC Cipher Used Greek alphabet (plus 3 old letters) in cipher system How does this extended system in order match up with ours? Primes...
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.

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