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Evolution of Numerals

Evolution of Numerals. By Evan Evans. Some ancient numbers. Ancient numbers. Limits of Four. Visual Limits. Humans have a visual distinguish “limit of four”. Different societies came up with ways to deal with this “limit of four”. Egyptian 3 rd Century BC. Cretan 1700-1200BC.

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Evolution of Numerals

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  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 3rd 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: aprinciple 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. I 20 XX 2 II 25 XXV 3 III 29 XIX 4 IV (IIII) 50 L 5 V 75 LXXV 6 VI 100 C 10 X 500 D 11 XI 1000 M 16 XVI Now try these: XXXVI 36 XL 40 XVII 27 DCCLVI 756 MCMLXIX 1969 Roman Numerals

  16. Roman Addition MMMDCCCI 3801

  17. Roman Subtraction CCXXXII 232

  18. Roman Multiplication MMMDCCL 3750

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

  20. 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

  21. Chronogram Activity

  22. Babylonian Maths The Babylonians

  23. Positional Notation

  24. BabylonIan =64 = 3604

  25. Numbers Traveled Through Exploration Through Trade Strong Arab Influence

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

  27. 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

  28. Based Traced Angles

  29. Which has Evolved into:

  30. 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

  31. 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 has Pigs at home

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

  33. 5 and 10

  34. Additive Angles 5 5 + 1 5 + 1 + 1 Write line 5 6 7

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

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

  37. Theory of 5-10

  38. Evolution in Persia The numbers evolved differently in Persia

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

  40. 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

  41. Rotation of the numerals

  42. Different dialects Arabic-Indic٠١٢٣٤٥٦٧٨٩ Eastern Arabic-Indic(Persian and Urdu) ۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹

  43. 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?

  44. Evolution of Numerals

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