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