1. Stories from the 400 Mathematical Tablets
Babylonia
Stories from the 400 Mathematical Tablets

2. Change of Rule
Babylonians invaded Mesopotamia replacing the Sumerians from around 2000 BCE
This was right after Sumerians revolted against the Akkadians (who ruled them previously)
Babylonian writing actually came from the Sumerians

3. Hammurabi Babylonian King Wrote the world’s first written code of law
On a pillar
Most of the Babylonian way of writing was
much more permanent than Egyptian.
Lots and Lots of Mud

4. The Tigris and Euphrates Rivers
3000 BC: Ending of Stone Age
Savannas were shrinking
Hunting and Gathering became inefficient
Why?
Overcrowding around oases
Danger of Starvation
Followed fleeing animals
Found Cradle between Rivers
Agriculture was born
Mesopotamia: “Between the Rivers”

5. Written Language necessary
Agriculture
Written Language necessary
Coordinate engineering tasks
Dams
Irrigation systems
Record-Keeping Systems
Weather Almanacs
Flood Seasons
New Technology
Leisure Time
For scribes, merchants, priests and royalty
Science and Math was born
Ploughing -

6. Babylonian Numerals
One
Ten

7. Used only two symbols to make all of these numbers
Babylonian Numbers
Grouping System
Used only two symbols to make all of these numbers

8. Babylonian Numbers >60
Positional System
Without placeholder “zero”
Positional System
With placeholder “zero”

9. Multiplication Tables by 9
Table Texts

10. Babylonian representation of Rational Numbers
Division: multiplication by the reciprocal
Used sexagesimal system for describing reciprocals
Reciprocal Tables

11. Base 60 1. Divide the base-10 number by 60, and record the remainder.
Divide the quotient from Step 1 by 60 again, and record the remainder.
Repeat the process until the quotient cannot be divided by 60 (in this case, the quotient will be 0 with a remainder of the original number).
The number, in base 60, will be the remainders in the reverse order.
Ex. Convert 148 to base 60
Ex. Convert 3, 20, 5 to base 10

12. Babylonian representation of Rational Numbers
Didn’t understand repeating decimals
Only made tables for factors of 60
2  0;30
3  0;20
9  0;6;40

13. How did Babylonians make their multiplication table?
Number
Square of Number 1 2 4 3 9 16 5 25 6 36 7 49 8
1,4
1,21 10
1,40 11
2,1 12
2,24
They had a square table
Used

14. Number
Square of Number 18
324 19
361 20
400 21
441 22
484 23
529 24
576 25
625 26
676 27
729 28
784 29
841 30
900

15. Yale Collection #7289 Very high approximation of
Convert 1:24, 51,10 to decimal
Yale tablet:

17. Why would Babylonians introduce the square root of 2 with this problem?
Remember, they were practical farmers!

18. Plimpton 322
Pythagorean Triples

19. Literal Translation Filled in missing piece Convert to decimal
Take third column squared minus second column squared
Divide the result by the third column squared

20. Generating Pythagorean Triples
Simplify

21. Algebraic Problem Solving
Take half of 1, which is 0;30,
Multiply 0;30 by 0;30, which is 0;15
Add this to 14,30 to get 14,30;15.
This is the square of 29;30
Now add 0;30 to 29;30 and the result if 30 – the side of square
Could solve algebraic equations
Didn’t use variables
To the right is a translation of a Babylonian tablet

22. Algebraic Problem
A canal 5 GAR long, 1 ½ GAR wide, and ½ GAR deep is to be dug. Each worker is assigned to dig 10 GIN, and is paid 6 SE. Find the area, volume, number of workers, and total cost.

23. Solution
Multiply length and width to get 7;30 SAR, the area. Multiply 7;30 by depth to get 45 SAR, the volume. Multiply the reciprocal of the assignment, 6, by 45 to get 4,30, which is the number of workers. Multiply 4,30 by the wages to get 9 GIN, the total expenses.

24. Sources
Felluga, Dino. Guide to Literary and Critical Theory. Purdue U, 28 Nov Web. 10 May 2006.
Eves, Howard. Introduction to the History of Mathematics. Pacific Grove,
Thomson Brooks/Cole: Print
Katz, Victor. A History of Mathematics, An Introduction. Boston,
Addison-Wesley: Print
Boyer, Carl. A History of Mathematics. Canada,
Wiley: Print
O’Connor, John. MacTutor History of Mathematics Archive, University of St Andrews, Scotland
JOC/EFR July Web. 12 Sept 2015
Allen, G. Donald. The History of Mathematicss, University of Texas A&M
Web. 12 Sept 2015