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Mesolithic Mesolithic and Neolithic and Neolithic tokens from tokens from the Middle the Middle
EastEastAs early as 9th millennium
the enigma of the sexagesimal the enigma of the sexagesimal systemsystem
► origin unknown but…vestiges origin unknown but…vestiges remain todayremain today
► numerous hypothesesnumerous hypotheses smallest number with greatest smallest number with greatest number of dividers number of dividers mixture of pre-existent base 10 andmixture of pre-existent base 10 and the new base 60 of emigrants the new base 60 of emigrants mystical reasons- cult of the mystical reasons- cult of the celestialcelestial god god
Long division Sumerian-Long division Sumerian-stylestyle
►Example from 2650 B.C. in Example from 2650 B.C. in ŠŠuruppakuruppak
►1,152,000 s1,152,000 sìla of barleyìla of barley
►Each person must get 7 Each person must get 7 ssìlaìla
►How many people will get barley?How many people will get barley?
Šàrgal-iá Šàr-u-minŠàrgal-iá Šàr-u-min1,152,0001,152,000
Literally means Literally means
216,000 x 5 + 36,000 x 2216,000 x 5 + 36,000 x 2
oror
5 x 605 x 6033 + 2 x (10 x 60 + 2 x (10 x 6022))
After the eclipse of After the eclipse of SumerSumer
BabyloniaBabylonia
►Everyday Babylonia strictly decimalEveryday Babylonia strictly decimal
►Stopped using calculiStopped using calculi
►Most probably had a counting deviceMost probably had a counting device
►Developed the rule of positionDeveloped the rule of position
►Developed the idea of zeroDeveloped the idea of zero