Mathematics in Mesopotamia TO5 - Weebly



Mathematics in Mesopotamia TO5

By Vickie Chao |   |[pic] | |[pic]

1     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 ([pic]) for 1 and 60. And they would express 70 ([pic]) as, literally, the sum of 60 ([pic]) and

10 ([pic]). Likewise, they would express 125 ([pic]) as the sum of two units of 60 ([pic]) and one unit of 5 ([pic]).

 

2     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.

 

3     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 ([pic]) and 6 ([pic]). 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.

 

4     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 [pic]. The left-most digit 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.

 

5     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!

Copyright © 2007 edHelper

[pic]

|Name _____________________________ | |[pic] |Date TO5___________________ |

Mathematics in Mesopotamia

|1.   |2.   |

|Which of the following about mathematics in Mesopotamia is correct? |How many minutes did the Sumerians say an |

|[pic]  The Sumerian numeral system is commonly known as the Arabic numerals. |hour has? |

|[pic]  The Sumerians counted things with twelve as a unit. |[pic]  30 |

|[pic]  People in Mesopotamia used a dot to denote zero. |[pic]  90 |

|[pic]  People in Mesopotamia said a full circle is equal to 360 degrees. |[pic]  15 |

| |[pic]  60 |

| | |

|3.   |4.   |

|How would people in Mesopotamia inscribe 10,925? |Which of the following statements is |

|[pic]  3 x 60 x 60 + 2 x 60 + 5 |correct? |

|[pic]  6 x 30 x 60 + 2 x 60 + 5 |[pic]  People in Mesopotamia did not apply |

|[pic]  12 x 30 x 30 + 4 x 30 + 5 |mathematics to their daily life. |

|[pic]  5 x 36 x 60 + 4 x 30 + 5 |[pic]  People in Mesopotamia developed |

| |their numerals around 500 A.D. |

| |[pic]  Hammurabi was an Assyrian King. |

| |[pic]  Mathematics began to take shape at |

| |the same time that the world's first |

| |civilization started to emerge in |

| |Mesopotamia. |

| | |

|5.   |6.   |

|How would the Sumerians write 65? |Who invented the world's first banking system? |

|[pic]  [pic] |[pic]  The Babylonians |

|[pic]  [pic] |[pic]  The Indians |

|[pic]  [pic] |[pic]  The Chinese |

|[pic]  [pic] |[pic]  The Arabs |

| | |

|7.   |8.   |

|Which two Sumerian numerals used the same symbol? |How would a Sumerian express the result of 80 minus |

|[pic]  1 and 32 |73? |

|[pic]  1 and 30 |[pic]  [pic] |

|[pic]  1 and 10 |[pic]  [pic] |

|[pic]  1 and 60 |[pic]  [pic] |

| |[pic]  [pic] |

| | |

|Name _____________________________ | |[pic] |Date ___________________ |

Mathematics in Mesopotamia

|9.   |10.   |

|Given that the Sumerians used a sexagesimal system, how many |Knowing that the Sumerian numeral system was a positional one, |

|days a year do you think a Sumerian calendar had? |what kind of large number does [pic]translate to? |

|[pic]  360 |[pic]  1,742,149 |

|[pic]  500 |[pic]  1,548,305 |

|[pic]  247 |[pic]  872,903 |

|[pic]  436 |[pic]  925,392 |

| | |

 

|Mathematics in Mesopotamia - Answer Key |

1  [pic]  People in Mesopotamia said a full circle is equal to 360 degrees.

2  [pic]  60

3  [pic]  3 x 60 x 60 + 2 x 60 + 5

4  [pic]  Mathematics began to take shape at the same time that the world's first civilization started to emerge in Mesopotamia.

5  [pic]  [pic]

6  [pic]  The Babylonians

7  [pic]  1 and 60

8  [pic]  [pic]

9  [pic]  360

10  [pic]  1,548,305

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download