Babylonian numerals Place Value Systems of Numeration

Babylonian numerals Place Value Systems of Numeration

Babylonian numerals

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See also: Babylonian mathematics

Babylonian numerals

Babylonian numerals were written in cuneiform , using a wedge-tipped 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 (base-60) 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]

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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 non-place-value 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 ( Babylonian 1.svg to count units and Babylonian 10.svg to count tens) were used to notate the 59 non-zero digits . These symbols and their values were combined to form a digit in a sign-value notation quite similar to that of Roman numerals ; for example, the combination Babylonian 20.svg Babylonian 3.svg represented the digit for 23 (see table of digits below). A space was left to indicate a place without value, similar to the modern-day 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 : Babylonian 20.svg Babylonian 3.svg 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 mixed-radix system of bases 10 and 6, since the ten sub-base was used merely to facilitate the representation of the large set of digits needed, while the place-values in a digit string were consistently 60-based 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 Babylonian digit 0.svg ) to mark the nonexistence of a digit in a certain place value.[ citation needed ]

See also[ edit ]

  • icon Mathematics portal
  • Ancient Near East portal
  • Babylon
  • Babylonia
  • History of zero
  • Numeral system

Notes[ edit ]

  1. ^ a b c Stephen Chrisomalis (2010). Numerical Notation: A Comparative History . p. 247.

  2. ^ a b Stephen Chrisomalis (2010). Numerical Notation: A Comparative History . p. 248.
  3. ^ http://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/

Bibliography[ edit ]

  • Menninger, Karl W. (1969). Number Words and Number Symbols: A Cultural History of Numbers. MIT Press. ISBN   0-262-13040-8 .
  • McLeish, John (1991). Number: From Ancient Civilisations to the Computer. HarperCollins. ISBN   0-00-654484-3 .

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 easy-to use numeral converter

Retrieved from ” https://en.wikipedia.org/w/index.php?title=Babylonian_numerals&oldid=870095303 ”
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  • Non-standard positional numeral systems
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