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

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. Main symbols (powers of 10)
Roman numbers
Main symbols (powers of 10)
Intermediate symbols 1 I 5 V 10 X 50 L
100 C
500 D
1000 M
Long form: MDCCCCLXXV =
Short form: MCMLXX1X =
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 1

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 2

22. Imaginary numbers
𝑖= −1

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
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!