1. History of Numbers

2. What Is A Number? What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?

3. 35,000 BC

4. Egyptian 3rd Century BC

5. Additive Numeral Systems Some societies have an additive numeral system: a principle of addition, where each character has a value independent of its position in its representation Examples are the Greek and Roman numeral systems

6. The Greek Numeral System

7. Roman Numerals

8. Drawbacks of positional numeral system Hard to represent larger numbers Hard to do arithmetic with larger numbers, trying do 23456 x 987654

9. South American Maths The Maya The Incas

10. twentiesunits Mayan Maths twentiesunits 2 x 20 + 7 = 47 18 x 20 + 5 = 365

11. Babylonian Maths The Babylonians

12. 3600s60s1s BabylonIanBabylonIan sixtiesunits =64 = 3604

13. Cultures that Conceived “Zero” Zero was conceived by these societies: Mesopotamia civilization 200 BC – 100 BC Maya civilization 300 – 1000 AD Indian sub-continent 400 BC – 400 AD

14. Hindu-Arabic We have to thank the Indians for our modern number system. Similarity between the Indian numeral system and our modern one

15. From the Indian sub-continent to Europe via the Arabs

16. Indian Numbers

17. Pythagoras’ Theorem 1 1 a a 2 = 1 2 + 1 2 So a 2 = 2 a = ? a 2 = b 2 + c 2

18. Square roots on the number line 01324567-2-3-4-5 √1√4√9 √2

19. Square roots of negatives √-1=i Where should we put √-1 ? 01324567-2-3-4-5 √1√4√9 √2

20. Imaginary numbers i 2i2i Real 3i3i 4i4i Imaginary 01324567-2-3-4-5 √1√4√9 √2