1. Evolution of Numerals By Evan Evans

2. Some ancient numbers

3. Ancient numbers

4. Limits of Four

5. Visual Limits Humans have a visual distinguish “limit of four”. Different societies came up with ways to deal with this “limit of four”.

6. Egyptian 3 rd Century BC

7. Cretan 1700-1200BC

8. England’s “five-barred gate”

9. Other Counting Methods The Elema of New Guinea Here is a figure to show you what some people have used

10. The Elema of New Guinea

11. Counting Sticks

12. Additive Numeral Systems Some societies have an additive numeral system: a principle of addition Each character has a value independent of its position in its representation Greek and Roman numeral systems

13. The Greek Numeral System

14. Arithmetic with Greek Numeral System

15. Roman Numerals 1I20 XX 2II25XXV 3III29XIX 4IV(IIII)50L 5V75LXXV 6VI100C 10X500D 11XI1000M 16XVI Now try these: 1. XXXVI 36 2.XL 40 3. XVII 27 4. DCCLVI 756 5. MCMLXIX 1969

17. Roman Addition MMMDCCCI CCLXIV +DCL +MLXXX +MDCCCVII 264 +650 +1080 +1807 3801

18. Roman Subtraction MMMDCCXXVIII -MDCCCLII -MCCXXXI -CCCCXIII CCXXXII 3728 -1852 -1231 -413 232

19. Roman Multiplication LXXV xL MMMDCCL 75 x50 3750

20. Chronograms “Time Writing” A sentence or Inscription in which the Capital or Highlighted Letters, interpreted in Roman Numerals, represent a particular date.

21. Chronogram “My Day Is Closed In Immortality” a chronogram commemorating the death of Queen Elizabeth the first. M D I C I I M D C I I I 1000+500+100+1+1+1 1603

22. Chronogram Activity

23. Babylonian Maths The Babylonians

24. Positional Notation …HundredsTensUnits 573

25. 3600s60s1s BabylonIanBabylonIan sixtiesunits =64 = 3604

26. Numbers Traveled Through Exploration Through Trade Strong Arab Influence

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

28. Roots of 1, 2, 3 and 4 In the West The Arabic numbers format are based traces with angles: Number one (1) has one angle. Number two (2) has two additives angles. Number three (3) has three additives angles. Number four (4) has four additive angles. The number four get closed due to cursive hand write

29. Based Traced Angles

30. Which has Evolved into:

31. Roots of 5 through 10 numbers: The circle is the symbol of the hand closed, which has five fingers. The number five was written under the write line. Joe has cows at home Write Line

32. TEN The number ten (the 2nd hand) was written (placed) on the top of write line. Theoretically, the circle on the top of the write line acquires double value (ten value). Joe hasPigs at home

33. Additive Angles Theory For each number above 5 you add 1 angle Or for a number below 10 you subtract an angle

34. 5 and 10

35. Additive Angles 5 5 + 1 5 + 1 + 1 675 Write line

36. Evolution of 5-6-7 in the West

37. Evolution of 8-9-10 in the West

38. Theory of 5-10

39. Evolution in Persia The numbers evolved differently in Persia

41. Evolution in the East In only 120 years the numbers had changed The numerals from al-Sizji's treatise of 969 The numerals from al-Biruni's treatise copied in 1082

42. The Evolution of 2-3 in the East The numerals of 2 and 3 have been rotated 90 degrees Scribes copied text in columns from top to bottom onto scrolls Scribes unfamiliar with Indian numerals

43. Rotation of the numerals

44. Different dialects Arabic-Indic ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩ Eastern Arabic-Indic (Persian and Urdu) ۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹

45. Questions to Ask Yourselves Is this the end of our number system? Are there going to be any more changes in our present numbers? In 300 years from now, will the numbers have changed again to be something else?

46. Evolution of Numerals