Two tablets found at Senkerah on the Euphrates in 1854 date from 2000 BC. Perhaps the most amazing aspect of the Babylonian's calculating skills was their construction of tables to aid calculation. As a base 10 fraction the sexagesimal number 5 25, 30 is 5 4/ 10 2/ 100 5/ 1000В which is written as 5.425 in decimal notation. We adopt the notation 5 25, 30 for this sexagesimal number, for more details regarding this notation see our article onВ Babylonian numerals.

5 hours, 25 minutes, 30 seconds, is just to write the sexagesimal fraction, 5 25/ 60 30/ 3600. This form of counting has survived for 4000 years. The Babylonians divided the day into 24 hours, each hour into 60 minutes, each minute into 60 seconds. For more details of the Babylonian numerals, and also a discussion as to the theories why they used base 60, see our article onВ Babylonian numerals. It was a positional system with a base of 60 rather than the system with base 10 in widespread use today. The Babylonians had an advancedВ number system, in some ways more advanced than our present systems. From the mathematicalВ point of viewВ these problems are comparatively simple. They are YBC 4666, 7164, and VAT 7528, all of which are written in Sumerian. There are several Old Babylonian mathematical texts in which various quantities concerning the digging of a canal are asked for. The rulers or highВ government officialsВ must have ordered Babylonian mathematicians to calculate the number of workers and days necessary for the building of a canal, and to calculate the total expenses of wages of the workers. It was an important task for the rulers of Mesopotamia to dig canals and to maintain them, because canals were not only necessary for irrigation but also useful for the transport of goods and armies. These are discussed in where Muroi writes:. For example we mentioned above the irrigation systems of the early civilisations in Mesopotamia. Many of theВ tabletsВ concern topics which, although not containing deep mathematics, nevertheless are fascinating. The later Babylonians adopted the same style of cuneiform writing on clay tablets. It was the use of a stylus on a clay medium that led to the use of cuneiform symbols since curved lines could not be drawn. Their symbols were written on wet clay tablets which were baked in the hot sun and many thousands of these tablets have survived to this day. The Sumerians had developed anВ abstract formВ of writing based on cuneiform (i.e. However theВ BabylonianВ civilisation, whoseВ mathematicsВ is the subject of this article, replaced that of the Sumerians from around 2000 BC The Babylonians were a Semitic people who invaded Mesopotamia defeating the Sumerians and by about 1900 BC establishing their capital at Babylon. The Sumerians, however, revolted against Akkadian rule and by 2100 BC they were back in control. The Akkadians invented the abacus as a tool for counting and they developed somewhat clumsy methods of arithmetic with addition, subtraction, multiplication and division all playing a part. Around 2300 BC the Akkadians invaded the area and for some time the more backward culture of the Akkadians mixed with the more advanced culture of the Sumerians. Writing developed and counting was based on a sexagesimal system, that is to say base 60.

This was an advanced civilisation building cities and supporting the people withВ irrigation systems, a legal system, administration, and even a postal service. The region had been the centre of the Sumerian civilisation which flourished before 3500 BC. Here is aВ map of the regionВ where the civilisation flourished.

185 in babylonian numerals