Babylonian numbering

Symbols used in Babylonian numeration.

The Mesopotamian numbering system is a system of representation of numbers in the cuneiform writing of various peoples of Mesopotamia, among them the Sumerians, the Akkadians and the Babylonians. a series of symbols

This system first appeared around 1800-1900 BCE. C. It is also credited as the first positional numeral system, that is, in which the value of a particular digit depends on both its value and its position in the number to be represented. This was an extremely important development, because, before the place-value system, technicians were forced to use unique symbols to represent each power of a base (ten, hundred, thousand, and so on), making even the most complex calculations possible. Unwieldy basics.

Although their system clearly had an internal decimal system, they preferred to use 60 as the third smallest unit instead of 100 as we do today. More appropriately, it is considered a mixed system of bases 10 and 60. A large value, having sixty as base, is the number that results in a smaller figure and that can also be divided without remainder by two, three, four, five and six, therefore also ten, fifteen, twenty and thirty. Only two symbols used in a variety of combinations were used to denote the 59 numbers. A space was left to indicate a zero (3rd century BCE), though they later devised a sign to represent a empty place.

The most commonly accepted theory is that 60, a number composed of many factors (the previous and next numbers in the series would be 12 and 120), was chosen as the base because of its 2×2×3× factorization 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 the integers from 1 to 6.

Integers and fractions were represented in the same way: the separator point for integers and fractions was not written, but was made clear by the context. And if we clarify the facts in Mesopotamia, it could be said that there was no zero.

For example, the number 53 in Babylonian numerals was represented using five times the symbol corresponding to 10 and 3 times the symbol corresponding to 1, as can be seen in the image above, or only 50 and 3.

Plimpton 322: Clay tablet dated to approximately 1900-1600 BC. of C. reveals that the Babylonians discovered a method to find Pythagorean triples, that is, sets of three integers such that the square of the largest of them is the sum of the squares of the other two. By the Pythagorean theorem, a triangle whose sides are proportional to all three (a Pythagorean triple) is a right triangle. Right triangles with sides proportional to the simpler Pythagorean triples turn up frequently in Babylonian problem texts, but if this tablet had not come to light, we would have had no reason to suspect that a general method capable of generating a number unlimited number of different Pythagorean triples was known from a millennium and a half before Euclid.