,
Babylonian
III
IU
Egyptian
Mayan
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lUI
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Greek
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-
Chinese
-- --II
Roman
Hindu
o
Arabic
•
,
r
Hindu-Arabic
o
1
2
III
~
#
IV
V
J "'l
4
.I"
VI
5
6
1/1
...!..!.!..
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VII
VIII
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9
10 A
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III III
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til'
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8
Mayan Numeration System
In warmer climates where people went
barefoot, people may have used their toes as well as their fingers for counting. The Mayans
introduced a new attribute that was present neither in the Egyptian nor in the Babylonian
systems, namely, a symbol for zero. The Mayan system used only three symbols, whi,~1
Table 3-4 shows.
TABLE 3-4
Mayan Numeral
Hindu-Arabic Equivalent
•
1
5
0
@
•••
-•-
}
13 • 20
-•-
+11- 1
~
}
+
16 • 20
o-
271
320 (a)
(b)
-•-
6 -360
= 2160
••
12 - 20
=
••••
1
9 -I
10 - 360 = 3600
240
=+
9
~
O· 20
••
2"1
=
0
=+
2
3602
2409
(a)
(b)
Roman Numeration System
Roman Numeral
Hindu-Arabic Equivalent
I
V
X
L
C
0
1
5
10
50
100
500
1000
M
DCLIX = (500
X
1000)
-Multipljc~tive
Roman Numeral
IV
IX
XL
XC
CO
CM
+ (100 + 50) +
Additive
Hindu-Arabic Equivalent
5
10
50
100
500
1000
(10 - 1) = 500,159
Subtractive
- 1, or 4
- 1, or 9
- 10, or 40
- 10, or 90
--100, or 400
- 100, or C
..
Egyptian Numeration Systenl
The Egyptian syst
.
em, datmg back to about 3400
..
. Egyptian Numeral
Vertical staff
Heel bone
Scroll
Lotus flower
Pointing finger
Polliwog or burbot
Astonished man
f'\
9
t
~
~
~
represents
represents
represents
represents
100,000
300
20
2
(\999nnll represents
100,322
~
99~
nn
II
tally marks.
Hindu-Arabic
Equivalent
Description
I
B. c., used
1
10
100
1000
10,000
100,000
1,000, ()()()
(100 + 100 + 100) (to + 10) (l + 1) Babylonian Numeration System
The Babylonian system was developed at about the same time as the Egyptian system. The
symbols shown in Table 3-3 were made using a stylus either vertically or horizontally.
TABLE 3-3
Babylonian Numeral
~
<
Hindu-Arabic Equivalent .
1
10
The Babylonian numerals 1 through 59 were similar to the Egyptian numerals, but the
staff and the heel bone were replaced by the symbols shown in Table 3-3.
For example,« 'f'f represented 22. For numbers greater than 59, the Babylonians used
place value.
« ,
<y <, f
, <f <, ,
represents
represents
represents
20 . 60 + 1, or 1201 11 ·60 - 60 + 11 - 60 + 1, or 40,261 1·60-60·60+ 11·60·60+ 11·60 + 1, or 256,261 ~allllumeraIs
http://www-groups.des.st-and.a c. uk. . .istTopics/B abyIonian_numerals.html
The Babylonian civilisation in Mesopotamia replaced the Sumerian civilisation and the Akkadian
civilisation. We give a little historical background to these events in our article Babvlonian mathematics.
Certainly in terms oftheif number system the Babylonians inherited ideas from the Sumerians and from
the Akkadians. From the number systems of these earlier peoples came the base of 60, that is the
sexagesimal system. Yet neither the Sumerian nor the Akkadian system was a positional system and this
advance by the Babylonians was undoubtedly their greatest achievement in terms of developing the
number system. Some would argue that it was their biggest achievement in mathematics.
Often when told that the Babylonian number system was base 60 people's first reaction is: what a lot of
special number symbols they must have had to learn. Now of course this comment is based on
knowledge of our own decimal system which is a positional system with nine special symbols and a zero
symbol to denote an empty place. However, rather than have to learn 10 symbols as we do to use our
decimal numbers, the Babylonians only had to learn two symbols to produce their base 60 positional
system.
Now although the Babylonian system was a positional base 60 system, it had some vestiges of a base 10
system within it. This is because the 59 numbers, which go into one of the places ofthe system, were
built from a 'unit' symbol and a 'ten' symbol.
Here
are 1
the 59
symbo s 2
built
from 3
these
two 4
symbo .~
5
6
7
8
r
11
rr
rrr­
~
W
ffl
•
W
12
13
14
15
16
<r
<rr
<rrr
21
22
23
«r
«rr
«rrr­
<~ 24«~
32
33
34
«r
«rr
«rrr­
36
26
27
18<W
28«W
9fW 19<m­
29
10 <
30
«
-«~
37
38«W
The 59 :ym!
40
42
~r
~
43
45~W
46~ffl
-«~ 47~~
«m­ 39 «m­
~
41
~rrr
«~ 44~~
<W 25«W 35«W
«ffl
<ffl «ffl
17<~
20
31
~
s of itle Baby1 oni an
48~W
49~m50
4
51
52
4r
4 rr
534rrr
544~
ss4W
564ffl
574~
584W
594m­
tiona1 system
..
Now gIven a pOSltional system one needs a conventIOn concernmg whIch end of the number represents
the units. For example the decimal 12345 represents
1 x 104
1 of 5
2 x 10 3 + 3 x 10 2 + 4 x 10 + 5.
217101 10:57 AM