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