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Counting on the fingers of one hand Donald Smith

Explore the ancient origins and evolution of counting, different number bases, fractions, and other types of numbers through a fascinating historical journey. From early markings and symbols to Egyptian, Babylonian, Roman, Mayan, and Hindu number systems, discover the principles, complexities, and interconnectedness of various numerical concepts. Delve into the world of negative numbers, irrational numbers, and even imaginary numbers. Expand your mathematical knowledge and get a deeper understanding of the diverse ways numbers shape our world.

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Counting on the fingers of one hand Donald Smith

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  1. Counting on the fingers of one handDonald Smith Faculty of Natural Sciences

  2. Outline • History of counting • Different number bases • Fractions • Other types of number

  3. Counting numbers The concept of the whole number is one of the oldest in mathematics and its origin is shrouded in the mists of prehistoric antiquity. A History of Mathematics Uta C Merzbach and Carl B Boyer

  4. Counting on the fingers of one hand • Grouped markings • Symbols before names • Common bases

  5. Egyptian numbers Credit: MacTutor St Andrews University

  6. Babylonian numbers • Base 60 – sexagesimal

  7. Roman numbers Long form: MDCCCCLXXV1111 = 1979 Short form: MCMLXX1X = 1979 Parts of a list: (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii) (xiii) (xiv) (xv)

  8. Mayan numbers Credit: MacTutor St Andrews University

  9. Hindu – Indian numbers • 9 symbols or ciphers or digits • Zero • “The earliest undoubted occurrence of a zero in India is in an inscription of 876” D E Smith, History of Mathematics, 1958

  10. 3 Principles of the “Hindu System” • Decimal base • Positional • 10 symbols, to include zero.

  11. Other bases • Duodecimal • Hexadecimal • Binary

  12. Guess the number

  13. Binary Sudoku

  14. Counting on the fingers of one hand

  15. Fractions • Egyptian • Babylonian • Greek

  16. Negative numbers • Debts • Timescale

  17. Multiplication of Negatives

  18. Multiplication of Negatives

  19. Multiplication of Negatives

  20. Multiplication of Negatives

  21. Irrational numbers • Pythagoras • Incommensurability • Hippasus of Metapontum

  22. Imaginary numbers

  23. Bibliography A History of Mathematics Uta C Merzbach and Carl B Boyer MacTutor History of Mathematics John J O’Connor and Edmund F Robertson http://turnbull.mcs.st-and.ac.uk/history Alex’s Adventures in Numberland Alex Bellos

  24. … and finally There are only 10 kinds of people those who understand binary … and those who don’t!

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