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history-page4 - • Two number systems ◦ Multiplicative...

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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 ... ◦ Di±erent for odd or even place Greek • Sparta settled in 1200 BC • Two number systems ◦ Attic ⋆ 500 BC ⋆ Acrophonic (used ²rst 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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