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Mathematics in Mesopotamia TO5
By Vickie Chao
Do you like mathematics? No matter what your answer may be, you are
not alone. Mathematics is a challenging subject. Its basic concepts began to
emerge when the world's very first civilization took root in Mesopotamia
more than 5,000 years ago. Back then, the Sumerians developed a unique
numeral system, using a base of sixty. In scientific terms, that system is
called a sexagesimal system. Since the Sumerians counted things with sixty
as a unit, they had the same symbol ( ) for 1 and 60. And they would
express 70 ( ) as, literally, the sum of 60 ( ) and
10 ( ). Likewise, they would express 125 (
) as the sum of two units
of 60 ( ) and one unit of 5 ( ).
1
Today, our decimal numeral system uses ten, not sixty, as a base unit.
But that is not to say that the Sumerians' invention became obsolete. As a
matter of fact, it still plays a critical role in our everyday life. For example,
have you ever wondered why an hour has 60 minutes and a minute has 60
seconds? Have you ever thought about why a full circle has 360 degrees? As
it turns out, that was how the Sumerians kept track of their time. And that
was how they defined a full circle.
2
When the Sumerians first came up with their numerals, they did not have
a specific symbol for zero. If they needed to inscribe, say, 506 on a clay
tablet, they would simply put a blank space between the symbols of 5 ( )
and 6 ( ). This way of denoting zero could be quite confusing and
problematic. Neither the Sumerians nor other people in Mesopotamia (most
notably, the Babylonians) were able to come up with a solution at the time.
This issue would remain unsolved until around 500 A.D. when the Indians
developed the Arabic numerals that we are still using today.
3
Even though the Sumerians and the Babylonians did not have a full grasp
of zero, they did introduce a groundbreaking concept - positional or place
value. Let's compare two numbers - 25 and 52. The symbol "5" of the first
number means 5 units, whereas "5" of the second number means 50. So, for
every position a digit moves to the left, it is increased by a power of 10. This
way of notation is for the Arabic numerals. But since both the Sumerians
and the Babylonians used a sexagesimal system, each of their digits would
be increased by a power of 60 as it moved along to the left. To express a
large number like 18,247, they would inscribe
. The left-most digit
4
equals to 5 times 60 times 60, or 18,000. The middle digit equals to 4 times
60, or 240. And the right-most digit equals to 7.
With their advanced knowledge in numerals, people in Mesopotamia
were excellent mathematicians. When applied to their daily life, they
developed formulas to calculate weights, areas, volumes, and wages.
Students from that time needed to study mathematics at school, too. They
had to learn how to do addition, subtraction, multiplication, division, and
fractions. During the reign of Hammurabi (1792 B.C. - 1750 B.C.) of the 1st
dynasty of Babylon, there were even specific laws addressing issues such as
interests and loans. Because of those codified rules, we know that people in
Mesopotamia were the ones who established the world's first banking system.
Without mastering mathematics, that would be entirely impossible!
5
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Name
_____________________________
Date
TO5___________________
Mathematics in Mesopotamia
1. Which of the following about mathematics in Mesopotamia is correct?
The Sumerian numeral system is commonly known as the Arabic numerals.
The Sumerians counted things with twelve as a unit.
People in Mesopotamia used a dot to denote zero.
People in Mesopotamia said a full circle is equal to 360 degrees.
2. How many minutes did the
Sumerians say an hour has?
30
90
15
60
3. How would people in Mesopotamia inscribe 10,925?
3 x 60 x 60 + 2 x 60 + 5
6 x 30 x 60 + 2 x 60 + 5
12 x 30 x 30 + 4 x 30 + 5
5 x 36 x 60 + 4 x 30 + 5
4. Which of the following
statements is correct?
People in Mesopotamia did
not apply mathematics to their
daily life.
People in Mesopotamia
developed their numerals
around 500 A.D.
Hammurabi was an Assyrian
King.
Mathematics began to take
shape at the same time that the
world's first civilization started
to emerge in Mesopotamia.
5.
How would the Sumerians write 65?
7. Which two Sumerian numerals used the same symbol?
1 and 32
1 and 30
1 and 10
1 and 60
6. Who invented the world's first banking
system?
The Babylonians
The Indians
The Chinese
The Arabs
8. How would a Sumerian express the
result of 80 minus 73?
Name _____________________________
Date ___________________
Mathematics in Mesopotamia
9. Given that the Sumerians used a sexagesimal
system, how many days a year do you think a
Sumerian calendar had?
360
500
247
436
10. Knowing that the Sumerian numeral system
was a positional one, what kind of large
number does
1,742,149
1,548,305
872,903
925,392
translate to?
Mathematics in Mesopotamia Answer Key
1
People in Mesopotamia said a full circle is equal to 360 degrees.
2
60
3
3 x 60 x 60 + 2 x 60 + 5
4
Mathematics began to take shape at the same time that the world's
first civilization started to emerge in Mesopotamia.
5
6
The Babylonians
7
1 and 60
8
9
360
10
1,548,305