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 in amman baccalaureate school.

The Babylonians, who were famous for their astrological observations and calculations (aided by their invention of the abacus), used a sexagesimal (base-60) positional numeral system inherited from the Sumerian and also Akkadian civilizations. Neither of the predecessors was a positional system (having a convention for which ‘end’ of the numeral represented the units).

This system first appeared around 3100 B.C.It is also credited as being the first known place-value 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 prior to place-value systems people were obliged to use unique symbols to represent each power of a base (ten, one-hundred, one thousand, and so forth), making even basic calculations unwieldy.

Only two symbols (one similar to a "Y" to count units, and another similar to a "<" 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 way similar to that of Roman numerals; for example, the combination "<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.

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, i.e. 60° in the angle of an equilateral triangle), minutes, and seconds in trigonometry and the measurement of time, although both of these systems are actually mixed radix.

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&times;2&times;3&times;5, which makes it divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. In fact, it is the smallest integer divisible by all integers from 1 to 6. Integers and fractions were represented identically &mdash; a radix point was not written but rather made clear by context.

Numerals

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.

Bibliography

*cite book
last = Menninger
first = Karl W.
year = 1969
title = Number Words and Number Symbols: A Cultural History of Numbers
publisher = MIT Press
id = ISBN 0-262-13040-8
*cite book
last = McLeish
first = John
year = 1991
title = Number: From Ancient Civilisations to the Computer
publisher = HarperCollins
id = ISBN 0-00-654484-3

See also

*Babylonia
*Babylon
*History of zero
*Numeral system

External links

* [http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html Babylonian numerals]
* [http://it.stlawu.edu/%7Edmelvill/mesomath/Numbers.html Cuneiform numbers]
* [http://mathforum.org/alejandre/numerals.html Babylonian Mathematics]
* [http://www.math.ubc.ca/%7Ecass/Euclid/ybc/ybc.html High resolution photographs, descriptions, and analysis of the "root(2)" tablet (YBC 7289) from the Yale Babylonian Collection]
* [http://it.stlawu.edu/%7Edmelvill/mesomath/tablets/YBC7289.html Photograph, illustration, and description of the "root(2)" tablet from the Yale Babylonian Collection]
* [http://demonstrations.wolfram.com/BabylonianNumerals/ Babylonian Numerals] by Michael Schreiber, The Wolfram Demonstrations Project.
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