Babylonian numerals
Jump to navigation
Jump to search
Babylonian numerals
Babylonian numerals were written in cuneiform , using a wedgetipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record.
The Babylonians , who were famous for their astronomical observations and calculations (aided by their invention of the abacus ), used a sexagesimal (base60) positional numeral system inherited from either the Sumerian or the Eblaite civilizations.^{ [1] } Neither of the predecessors was a positional system (having a convention for which ‘end’ of the numeral represented the units).
Contents
 1 Origin
 2 Characters
 3 Zero
 4 See also
 5 Notes
 6 Bibliography
 7 External links
Origin[ edit ]
This system first appeared around 2000 BC;^{ [1] } its structure reflects the decimal lexical numerals of Semitic languages rather than Sumerian lexical numbers.^{ [2] } However, the use of a special Sumerian sign for 60 (beside two Semitic signs for the same number)^{ [1] } attests to a relation with the Sumerian system.^{ [2] }
Numeral systems 

Hindu–Arabic numeral system 

East Asian 

Alphabetic 

Former 

Positional systems by base 

Nonstandard positional numeral systems 

List of numeral systems 

Characters[ edit ]
The Babylonian system is credited as being the first known positional numeral system , in which the value of a particular digit depends both on the digit itself and its position within the number. This was an extremely important development, because nonplacevalue systems require unique symbols to represent each power of a base (ten, one hundred, one thousand, and so forth), which can make calculations more difficult.
Only two symbols ( to count units and to count tens) were used to notate the 59 nonzero digits . These symbols and their values were combined to form a digit in a signvalue notation quite similar to that of Roman numerals ; for example, the combination represented the digit for 23 (see table of digits below). A space was left to indicate a place without value, similar to the modernday zero . Babylonians later devised a sign to represent this empty place. They lacked a symbol to serve the function of radix point , so the place of the units had to be inferred from context : could have represented 23 or 23×60 or 23×60×60 or 23/60, etc.
Their system clearly used internal decimal to represent digits, but it was not really a mixedradix system of bases 10 and 6, since the ten subbase was used merely to facilitate the representation of the large set of digits needed, while the placevalues in a digit string were consistently 60based and the arithmetic needed to work with these digit strings was correspondingly sexagesimal.
The legacy of sexagesimal still survives to this day, in the form of degrees (360° in a circle or 60° in an angle of an equilateral triangle ), minutes , and seconds in trigonometry and the measurement of time , although both of these systems are actually mixed radix.^{ [3] }
A common theory is that 60 , a superior highly composite number (the previous and next in the series being 12 and 120 ), was chosen due to its prime factorization : 2×2×3×5, which makes it divisible by 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , and 30 . Integers and fractions were represented identically — a radix point was not written but rather made clear by context.
Zero[ edit ]
The Babylonians did not technically have a digit for, nor a concept of, the number zero . Although they understood the idea of nothingness , it was not seen as a number—merely the lack of a number. What the Babylonians had instead was a space (and later a disambiguating placeholder symbol ) to mark the nonexistence of a digit in a certain place value.^{[ citation needed ]}
See also[ edit ]
 Babylon
 Babylonia
 History of zero
 Numeral system
Notes[ edit ]
 ^ ^{a} ^{b} ^{c} Stephen Chrisomalis (2010). Numerical Notation: A Comparative History . p. 247.
 ^ ^{a} ^{b} Stephen Chrisomalis (2010). Numerical Notation: A Comparative History . p. 248.
 ^ http://www.scientificamerican.com/article/expertstimedivisiondayshoursminutes/
Bibliography[ edit ]
 Menninger, Karl W. (1969). Number Words and Number Symbols: A Cultural History of Numbers. MIT Press. ISBN 0262130408 .
 McLeish, John (1991). Number: From Ancient Civilisations to the Computer. HarperCollins. ISBN 0006544843 .
External links[ edit ]
Wikimedia Commons has media related to Babylonian numerals . 
 Babylonian numerals
 Cuneiform numbers
 Babylonian Mathematics
 High resolution photographs, descriptions, and analysis of the root(2) tablet (YBC 7289) from the Yale Babylonian Collection
 Photograph, illustration, and description of the root(2) tablet from the Yale Babylonian Collection
 Babylonian Numerals by Michael Schreiber, Wolfram Demonstrations Project .
 Weisstein, Eric W. “Sexagesimal” . MathWorld .
 CESCNC – a handy and easyto use numeral converter
 Babylonian mathematics
 Nonstandard positional numeral systems
 Numeral systems
 Numerals
 All articles with unsourced statements
 Articles with unsourced statements from May 2015
 Commons category link is on Wikidata
Navigation menu
 This page was last edited on 22 November 2018, at 09:58 (UTC).
 Text is available under the Creative Commons AttributionShareAlike License ;
additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy . Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. , a nonprofit organization.
 Privacy policy
 About Wikipedia
 Disclaimers
 Contact Wikipedia
 Developers
 Cookie statement
 Mobile view