1. Why base 10 ?

2. The most common base in history

3. Conflicting forces TheoreticianPragmatist

4. Tigris-Euphrates River Valley

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

6. Pictograms

7. Development of Pictograms into Cuneiform

8. Archaic Sumerian numbers 11060600 3 60036 000

9. Ancient Sumerian Writing

10. Bulla, Calculus, and Seals

11. Bulla: binding contracts in an illiterate society

12. the enigma of sexagesimal base

13. 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

14. 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?

15. Šà rgal-i á Šà r-u-min 1,152,000 Literally means Literally means 216,000 x 5 + 36,000 x 2 or or 5 x 60 3 + 2 x (10 x 60 2 )

16. how the Sumerians did their sums

17. Calculation with pellets, cones, and spheres

23. 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

24. Babylonian positional numbering