|
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 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 1900 BC to 1800 BC. 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 "< 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: 2×2×3×5, 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 — a radix point was not written but rather made clear by context.
Numerals
Bibliography See also | ||||||||||
|
| |||||||||||
 |
|
| |