Babylonians
Wrote in
cuneiform (wedge) pattern of writing on soft clay
tablets
The
Babylonians divided the day into 24 hours, each hour into 60 minutes,
each
minute into 60 seconds. This form of counting has survived for 4000
years.
Thus,
base 60 but the 59 numerals were built with only 2 symbols
Cuneiform
numbers were written using a combination of just two signs: a vertical
wedge
for '1' and a corner wedge for '10'.
They used no zero
Egyptians
The
Egyptians had a base 10 system of hieroglyphs for numerals.
There
was no symbol for zero
They
had seven separate symbols (hieroglyphs) for one unit, one ten, one
hundred,
one thousand, one ten thousand, one hundred thousand, and one million
as shown
below:
Greeks
2
systems of numbers
Within
this system the Greeks were the first to show the use of a multiplier
by
combining symbols like this
The
Greeks also used a numeral system based on the 27 letters in the Greek
alphabet. In order to differentiate between numeral and letter, when
letters
are written to represent numbers, a bar was put over the symbol to
distinguish
it from the corresponding letter.
Incas
The
Inca people numbered around 12 million but they were from many
different ethnic
groups and spoke about 20 different languages. The civilization had
reached a
high level of sophistication with a remarkable system of roads,
agriculture,
textile design, and administration. Of course even if writing is not
required
to achieve this level, counting and recording of numerical information
is
necessary. Thus, the Incas had developed a method of recording
numerical
information which did not require writing. It involved knots in strings
called quipu. The quipu was
not a
calculator; rather it was a storage device. Remember that the Incas had
no
written records and so the quipu played a major role in the
administration of
the Inca empire since it allowed numerical information to be kept. The
quipu
consists of strings which were knotted to represent numbers. A number
was
represented by knots in the string, using a positional base 10
representation.
If the number 586 was to be recorded on the string then six touching
knots were
placed near the free end of the string, a space was left, then eight
touching
knots for the 10s, another space, and finally 5 touching knots for the
100s.
Romans
The
Romans used 7 symbols to express their number system
|
character |
numerical
value |
|
I |
1 |
|
V |
5 |
|
X |
10 |
|
L |
50 |
|
C |
100 |
|
D |
500 |
|
M |
1000 |
There
was no symbol for zero
The
Romans used the idea of subtraction to write numerals. When a smaller
numeral
is on the left of a larger numeral you take the difference. For
example, IV = 5
Ð 1 = 4
Later Romans
used a horizontal line above a particular
numeral to represent one thousand times that numeral, and additional
vertical
lines on either side of the numeral to denote one hundred times the
number, as
in these examples:
Indians
They
were the first to develop a base ten system. They developed methods of
expressing every possible number using a set of ten symbolsÉ
very similar to
the decimal system we use today with symbols close to the ones we use
today.
Zero
was used to denote an empty space.
The
scales of measurement used in India are similar to the scales we use
today.
Example: ÒIndus Inch = 1.32 inches in our system)
Mayans
The
Mayans discovered/developed zero!
The
had a 365 day calendar like ours
The
numeral system was base 20. Almost certainly the reason for base 20
arose from
ancient people who counted on both their fingers and their toes.
Although it
was a base 20 system, called a vigesimal system, one can see how five
plays a
major role, again clearly relating to five fingers and toes. In fact it
is
worth noting that although the system is base 20 it only has three
number
symbols (pebble, stick and shell). The shell represented zero as a
place holder
and as a quantity
Arabic
The
Indian numerals form the basis of the European number systems which are
now
widely used. However they were not transmitted directly from India to
Europe
but rather came first to the Arabic/Islamic peoples and from them to
Europe. The
story of this transmission is not, however, a simple one. The eastern
and
western parts of the Arabic world both saw separate developments of
Indian
numerals with relatively little interaction between the two. By the
western
part of the Arabic world we mean the regions comprising mainly North
Africa and
Spain. Transmission to Europe came through this western Arabic route,
coming
into Europe first through Spain.
The
form of the numerals in the west of the Arabic empire look more
familiar to
those using European numerals today which is not surprising since it is
from
these numerals that the Indian number system reached Europe.