Why base 10 ?. The most common base in history Conflicting forces TheoreticianPragmatist.

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Presentation transcript:

Why base 10 ?

The most common base in history

Conflicting forces TheoreticianPragmatist

Tigris-Euphrates River Valley

Mesolithic and Neolithic tokens from the Middle East As early as 9 th millennium

Pictograms

Development of Pictograms into Cuneiform

Archaic Sumerian numbers

Ancient Sumerian Writing

Bulla, Calculus, and Seals

Bulla: binding contracts in an illiterate society

the enigma of sexagesimal base

the enigma of the sexagesimal system ► origin unknown but…vestiges remain today ► numerous hypotheses  smallest number with greatest number of dividers  mixture of pre-existent base 10 and the new base 60 of emigrants  mystical reasons- cult of the celestial god

Long division Sumerian-style ►E►E►E►Example from 2650 B.C. in Šuruppak ►1►1►1►1,152,000 sìla of barley ►E►E►E►Each person must get 7 sìla ►H►H►H►How many people will get barley?

Šà rgal-i á Šà r-u-min 1,152,000 Literally means Literally means 216,000 x ,000 x 2 or or 5 x x (10 x 60 2 )

how the Sumerians did their sums

Calculation with pellets, cones, and spheres

After the eclipse of Sumer Babylonia ► Everyday Babylonia strictly decimal ► Stopped using calculi ► Most probably had a counting device ► Developed the rule of position ► Developed the idea of zero

Babylonian positional numbering