1. Early Numeration Systems Simple Systems Place Value Systems

2. Why start here? Who had the first numeration system? Why are they important?

3. Mathematical System 1. Elements, Symbols 2. Operations on the elements 3. Compare the elements Counting numbers

4. Egyptians – uses pictorial symbols called hieroglyphics Additive System – any given number is written by using numerals whose sum equals the number.

5. stroke heel bone scroll lotus flower pointing finger fish astonished person

6. Copied from original, 2000BC 85 math problems Alexander Rhind Scottish amateur archeologist, purchased it in 1858.

7. I ones V fives X tens L fifty C one hundred (centum – century) D five hundred M one thousand (mille, millennium)

8. Tablet with mathematics on it. Two symbols;

9. Pythagoras triples – Babylonian tablet

10. Numeration system is base 60. They have a place values, in groups of 60 Why is it based on 60? 1. 360 degrees is in a circle 2. Time: 24 hours in a day, 60 minutes for each hour, 60 seconds for each minute.

11. Based on 20 with 18 20 = 1 20 = 20 18 * 20 = 360 18 * 20 = 7200

12. Based on 10, place values are powers of 10 Symbols are called digits, we have 10 fingers

13. Abu Ja’far Muhammad ibn Musa al’Khwarizmi: 790 A.D. – 850 A.D. Wrote two texts about the new number system Translated into Latin in 12 th century in Europe.

14. Algorists – people for the new system Abacists – people against the new system. The numbers evolved from additive angles (1, 2, 3, 4) and the abacus manuscript notation (5, 6, 7, 8, 9, 0).