1. The History of Numbers

2. Introduction Numbers serve two purposes
Tools for Counting and Measuring
Attempt to Understand the Unexplainable
Natural versus Learned Counting
Develop System & Method of Manipulation
Linguistics to Communicate the System

3. Introduction
Civilizations each developed their own system, each contributing to today’s understanding of numbers

4. Babylonian Numbers Some of the Earliest Devices to Record Calculations
Clay Tablets in Iran of Base 10
Clay Tablets in Iraq of Base 60
Both Counting Systems are Still Present in Society Today

5. Egyptian Numbers
Number System is not well evidenced, but their contribution is undeniable
The Temple of Wasat was the World’s first University
Educated 80,000 students at its peak
Students included: ???

6. Egyptian Numbers
Students included: Plato, Aristotle, Socrates, Euclid, Pythagoras, Hypocrates, Archimides, Euripides

7. Egyptian Numbers Left Little Written Evidence of Mathematics
Rhind Papyrus (1650 BCE)
Scroll 20’ x 1’ with 87 problems

8. Greek Numbers Which is more basic: Arithmetic or Geometry?
Discrete or Continuous Universe
Reality is Mathematical in Nature
Irrational Numbers Presented a Philosophical Problem for the Greeks
Thinking Based on Words and Abstract Diagrams

9. Greek Numbers
By 500 BCE, they had a system based on the decimal and comprised of the 27 letters of their alphabet
First nine letters represented the digits 1-9
Second nine represented the tens

10. Greek Numbers The last nine represented the hundreds
Special sign for numbers higher than 900
There was no zero
Numbers were nonpositional

11. Roman Numbers Roman numerals spread throughout Western Europe
Started with stick numbers (I, II, III, IIII)
Added six letter symbols (V, X, L, C, D, M)
Addition & Subtraction were simple, but Multiplication & Division proved Complicated
CCKCVI + DCL + MLXXX = ?

12. Roman Numbers The Abacus existed to provide place value
Work vanished as it was performed, leaving no record of the process
No way to check results other than to redo the calculation

13. Arabic Numbers
In 830, Caliph al’Mamun founded the House of Wisdom in Baghdad
Advancement during European Dark Ages
Muslim world was reading translated works of the great Greek mathematicians

14. Arabic Numbers
Arabic numerals were promoted by Fibonacci, but met opposition in Europe
System had place value and zero

15. Mayan Numbers
Employed a place value system with a base twenty counting system
They used a dot to represent 1 and a horizontal line for 5
Larger numbers were represented by stacking symbols in columns
Had a zero