The ancient Babylonians conducted their explorations into the world of mathematics through the use of cuneiform, or wedge-shaped writing. They had two symbols: a vertical line standing for units, roughly approximated by "|", and an angular wedge representing tens, similar to "<". Thus the numeral <<|| might represent the value twenty-two. For more realistic representations of what Babylonian cuneiform actually looked like, try visiting:
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html

The Babylonians inherited their number system from their regional ancestors, the Akkadians and the Sumerians. Most interesting about this system is that it is conducted in base 60, or hexagesimal (Or sexagesimal thanks Jurph) as it is technically known. Thus, where our Arabic numeral system consists of units, tens, hundreds, thousands, etc., the Babylonian system would look something like this:

|| ; <<||| ; <<<||
^3600s ^60s ^units

Thus the total value of the above numeral would be 2*3600+23*60+32=7200+1380+32=8,612.

While this system may seem complicated to us, that is merely because we are so accustomed to working in base 10. Interestingly enough, we have inherited the hexagesimal system from the Babylonians in our measurements of time (seconds, minutes, hours) and angles (seconds, minutes, degress).

The Babylonians had no explicit character for the floating point (which might be called the hexagesimal point in this system). That is, there was no symbol to the left of which numerals represented whole numbers and to the right of which numerals represented fractions. The Babylonians did, however, employ fractional values; the location of the floating point was implied by context.

In addition, the Babylonians did not employ a symbol for zero, so that the representations of 1, 60, 3600, were all identical: "|". Again, this confusion was resolved by context. In multi-digit numbers, spacing was used to mark null place-values.

In addtion to a well-developed numeral system, the Babylonians had a reasonably advanced knowledge of Geometry. The two most famous cuneiform tablets unearthed by Archaeologists are the Plimpton 322 and the Yale tablets. On these and other tablets, geometrical diagrams of squares and triangles reveal a deep understanding of the Pythagorean Theorem. In addition, ancient Babylonians calculated sqrt(2) accurately to within 5 decimal places! Authors are not certain the algorithm by which this approximation was obtained. Regardless, it is clear that although the Babylonian system of numerals is very different from our own, these ancient people nevertheless had a deep comprehension of geometry and algebra.

Sources:
Personal knowledge and
O'Connor, J.J., and Robertson, E.F. "Babylonian Mathematics." Online available
http://www-history.mcs.st-andrews.ac.uk/history/Indexes/Babylonians.html

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