1. Babylonia Stories from the 400 Mathematical Tablets

2. 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 Eves, Howard. History of Mathematics

3. 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 -http://www.crystalinks.com/sumeragriculture.html

4. Babylonian Numerals OneTen

5. Babylonian Numbers 1 - 59 Grouping System Used only two symbols to make all of these numbers Try to fill in the missing blanks on your white boards.

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

7. Multiplication Tables by 9

8. For what number is this a multiplication table?

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

10. Babylonian representation of Rational Numbers Didn’t understand repeating decimals Only made tables for factors of 60 Top line reads: 1, its 2/3, 40 it is Second line reads: its half, 30 it is The opposite of: 3 is :20 4 is :15 5 is: 12 6 is :10

11. On your white boards Represent the numbers to the right in sexagesimal

12. How did Babylonians make their multiplication table? NumberSquare of Number 11 24 39 416 525 636 749 81,4 91,21 101,40 112,1 122,24 They had a square table Used

13. On your whiteboard NumberSquare of Number 18324 19361 20400 21441 22484 23529 24576 25625 26676 27729 28784 29841 30900

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

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

17. Plimpton 322 Pythagorean Triples

18. 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 http://public.csusm.edu/Aitken_html/m330/Meso/Plimpton322.trans.gif

19. Generating Pythagorean Triples Simplify Could this be how the Babylonians generated their Pythagorean triples?

20. Algebraic Problem Solving 1. Take half of 1, which is 0;30, 2. Multiply 0;30 by 0;30, which is 0;15 3. Add this to 14,30 to get 14,30;15. 4. This is the square of 29;30 5. No 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

21. Babylonian solution to

23. Sources Eves, Howard. Introduction to the History of Mathematics. Pacific Grove, Thomson Brooks/Cole: 1990. Print Katz, Victor. A History of Mathematics, An Introduction. Boston, Addison-Wesley: 2009. Print Boyer, Carl. A History of Mathematics. Canada, Wiley: 1989. Print Felluga, Dino. Guide to Literary and Critical Theory. Purdue U, 28 Nov. 2003. Web. 10 May 2006. O’Connor, John. MacTutor History of Mathematics Archive, University of St Andrews, Scotland JOC/EFR July 2015. Web. 12 Sept 2015 Allen, G. Donald. The History of Mathematicss, University of Texas A&M 2002-2014. Web. 12 Sept 2015