1. Ancient Number Systems
A Brief Overview

2. In The Beginning One and Many
Men needed new numbers, so they strung them together
The Bacairi and Bororo of Brazil string numbers-words together
- one, two, two and one, two and two, etc.

3. Dem Dry Bones Tally Sticks Ishango Bone - 18,000 BC
30,000 year-old wolf bone in Czechoslovakia
- 55 notches arranged in groups of 5

4. Counting with Body Parts
Five was popular
“Fiving” was used by the Greeks to describe tallying
Our decimal system started by counting on our fingers
Some ancient cultures used a base-20 or vigesimal system
- This came from counting fingers and toes

5. Why Count?
Property
Trading
Time
Measuring
Etc…

6. Egyptian Numerals

7. Overview Possible the first to practice science Base 10
Not positional, had no zero
Measuring and Surveying
Nile floods
Taxes
Mostly they used geometry

8. Symbols

9. Fractions and Operations
They had ways of expressing unit fractions (the numerator is 1) and common fractions such as 3/4 and 2/3
They also had addition and subtraction

10. Babylonian Numerals

11. Overview Sexagesimal (base 60) system
Measured circles and spheres using 360 equal parts.
Famous for astronomical observations and calculations
They invented the abacus

12. Overview Continued First known positional system
- Numbers arranged in columns
60 is a superior highly composite number
Divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30
Powers of 60 instead of 10
No symbol for 0, instead used a different place holder:

13. Symbols

14. Positional System

15. Roman Numerals

16. Overview Written using letters from the Latin alphabet
This is a biquinary system (base 10 with sub-base 5)
Use an additive and subtractive system
Example:
- IV = 4, 1 before 5

17. Subtraction Rules
Subtract only powers of 10, such as I (100), X (101) or C (102). VL = 45 is not allowed
Subtract only one numeral from one numeral. Write VIII for 8, not IIX. 19 is XIX, IXX
Don’t subtract a letter from another letter more than 10 times greater. MIM is “illegal”, you can only subtract I from V or X, X from L or C, and C from M

18. Legacy of Roman Numerals
Hour marks on timepieces
Sequels of movies, video games, and other works (ex: Star Wars IV: A New Hope)
Book volume and chapter numbers
Page numbering and outlines
Occurrances of large recurring events:
-The Olympic Games (XXXI Winter Games)
- The Super Bowl (XLVII)

19. Legacy Continued Monarchs and Popes (Elisabeth II, Pope Benedict XVI)
Generational Suffixes (Ex: Thurston Howell III)
Year of construction on cornerstones
And many more uses

20. Greek Numbers

21. Overview Used letters as numbers Didn’t have zero
You had to memorize addition facts
Multiplication was worse
Numerology was common because they used their letters for their alphabet
Now we use Greek letters for specific numbers
- π and ф (the golden ratio)

22. Symbols

23. Mayan numerals

24. Overview Place value (positional) number system Base 20 (vigesimal)
They have a 0
They used rows instead of columns
Shells, sticks and pebbles

25. Symbols

26. Operations They had addition and subtraction
You will have a chance to try operations with Mayan Numerals later this week

27. Calendar
The Solar Calendar in the Calendar Round; called the Haab, is extremely accurate
Each month was 20 days and they had 18 months
There was a 5 day period called Uayeb or Wayeb that was unlucky
The Western calendar was created with no year 0
- This caused a controversy of the precise start of the millennium.

29. Chinese Numerals

30. Overview Mathematics was considered both pracitcal and spiritual
- Covered everything from administration and water control to religion and astronomy
Art of Calculation
Base 10
“Nine Chapter on the Mathematical Art” 200 BC

31. Shang Oracle Bone 14th Century BC

32. Counting Rod Numerals

33. Zero They understood zero, but didn’t have a symbol
To deal with a placeholder, they would use a reckoning board, with an empty square to signify 0.

34. Hindu-arabic numerals

35. Overview These are the numbers we use now Positional decimal system
A stone inscription found at Chaturbhuja Temple at Gwalior in India is the first instance of 0.
The oldest known writing using a fully develop numeration system appears in a book from AD 825 by Persian Mathematician al-Khowarizmi

37. Fibonacci
Fibonacci is also know as Leonardo of Pisa is an Italian mathematician
Made Hindu-Arabic Numerals popular in Europe
Liber Abaci (“The Book of Calculation”)

38. “My father was a public scribe of Bejaia [Algeria], where he worked in Customs, defending the interests of Pisan merchants who made their fortune there. He made me learn how to use the abacus when I was still a child because he saw how I would benefit from this in later life. In this way I learned the are of counting using the nine Indian figures…as follows: 9, 8, 7, 6, 5, 4, 3, 2, 1, … With these nine numerals, and with this sign 0, called zephirum in Arabic, one writes all the numbers one wishes. - Leonardo of Pisa