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History of Numbers

History of Numbers. What Is A Number?. What is a number? Are these numbers? Is 11 a number? 33? What about @xABFE?. 35,000 BC. Egyptian 3rd Century BC. Additive Numeral Systems.

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History of Numbers

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  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 AmericanMaths The Maya The Incas

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

  11. Babylonian Maths The Babylonians

  12. BabylonIan =64 = 3604

  13. Culturesthat 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 a2 = b2 + c2 a2 = 12 + 12 Soa2 = 2 a= ? a 1 1

  18. Square roots on the number line √1 √4 √9 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 √2

  19. Square roots of negatives Where should we put √-1 ? √-1=i √1 √4 √9 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 √2

  20. Imaginary numbers 4i 3i Imaginary 2i i √1 √4 √9 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Real √2

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