1. Keeping Count Writing Whole Numbers
Sketch 1
Keeping Count
Writing Whole Numbers

2. Early Counting Tally Bones Bodily Mathematics Finger Counting
Number Words & Body Parts

3. Egyptian Mathematics
Hieroglyphics (2700 BC)
Hieratic Script

4. Egyptian Mathematics What is important about Egyptian mathematics?
Ancient Egyptian Mathematics
Egyptian Fractions
Egyptian Numbers

5. Egyptian Mathematics Materials for writing Papyrus made of reeds
Leather
Cloth like cotton or linen
Stone

6. Egyptian Mathematics Rhind Papyrus
In the middle of the Hyksos period, a scribe named Ahmose wrote a treatise on Egyptian mathematics
Ahmose Papyrus or Rhind Papyrus (after the man who purchased it)
Most comprehensive Egyptian document that still exists as a complete work

7. Egyptian Mathematics Rhind Papyrus 18 ft by 13 inches
Probably written around 1650 BC
Ahmose claimed his work was based on the work of an older manuscript that was never found
May or may not have been Ahmose’s work
To make it more likely that a person’s work would be copied in the future, one might claim it was the work of a great thinker of the past

8. Egyptian Mathematics Complete 387 + 245 using Egyptian hieroglyphics.

9. Egyptian Mathematics Multiplication
Multiplication and division were the first mathematical operations described in the Rhind papyrus
Not explained, but work was shown
Multiplication = repeated addition
Doubling and halving

10. Egyptian Mathematics
Multiplication
Example: 27 x 34

11. Babylonian Mathematics
Area between the Tigris and Euphrates rivers—modern day Iraq
In about 3000 BC the Sumerians developed as a group of city states close to the Persian Gulf
Ur was the best know city state
Each city state was its own political entity, which made it easy to conquer these

12. Babylonian Mathematics
Eight different civilizations inhabited this area over the years of 3000 BC to about 300 BC when Alexander the Great died and the regions around the Fertile Crescent were ruled by general Seleucus.
Sumerians
Akkadians
Amorites
Hittites
Assyrians
Chaldeans
Persians
Seleucids
We often inaccurately refer to all of this as “Babylonia.”

13. Babylonian Mathematics
The Sumerians were the ones who invented the method of writing known as cuneiform or “wedge-shaped” by pressing a stylus into wet clay. They baked the tablets to preserve them.
More than ½ million clay tablets exist today.
There was trade in Mesopotamia and the need for irrigation. Thus, much of their mathematics dealt with the digging of canals. The lack of isolation in Mesopotamia, vs Egypt, affected their mathematics.

14. Babylonian Mathematics
Notation and Computation:
Two symbols, one for units and one for tens
Base 60 positional system—sexagesimal
What we will discuss are the symbols used during just one time period. There were changing all the time and looked different at different times and in different places in Mesopotamia.
Babylonian Mathematics

15. Babylonian Mathematics
Write the following numbers in Babylonian, base 60, system. 22 84 62
614
Write 3, 42, 31; in our number system, base 10.

16. Babylonian Mathematics
What are some problems with the Babylonian number system?

17. Maya Mathematics
Two symbols, a dot for one and a line or bar for five (p. 67)
Maya Mathematics
Arranged vertically instead of horizontally and placed the place value amounts in each group
The groups were:
1-19
20s
18 x 20
18 x 202
18 x 203
etc
Used a zero for an empty place value.
Due to their lack of contact with Europe, their numeration system had no influence on European numeration.
Maya PowerPoint.

18. Maya Mathematics
Try writing 43,274 using Mayan symbols

19. Roman Number System Roman numerals Used subtraction
Larger numbers get a bar overtop of the number
For example, a V with a bar over it would be 5 x 1000 = 5000
A V with two bars over it would be 5 x 1000 x 1000 = 5,000,000

20. Greek Number System Greek Number Systems More on Greek Number Systems
Used their Greek alphabet plus two/three other symbols (450 BC)
Nine symbols for the units, nine symbols for the tens, and nine for the hundreds
Special mark used for numbers over 1000

21. Greek Number System Greek Number Systems More on Greek Number Systems
Used uppercase letters and then lowercase letters
Since they also used alphabet for words, they put a bar over alphabet letters used to represent numbers
Used a large M, myriad or myrioi, for and then put correct symbol over the M for a larger number.
For example, an M with the symbol for 4 over the M would be

22. Greek Number System 98,375 would be:
written in lowercase Greek alphabet
written in uppercase Greek alphabet

23. Current Number System Hindu Arabic Number System
Invented by the Hindus sometime before 600 AD and refined over time
Picked up by Arabs during Islamic expansion into India in 7th and 8th centuries
Europeans took it from the Arabs
Basic symbols are 0-9 and called digits
Roman number system existed for a long time
Worried about changing 2 to 20 (theft)
Hard to compute with Roman numerals—they used an abacus