Evolution of Numerals By Evan Evans. Some ancient numbers.
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Transcript of Evolution of Numerals By Evan Evans. Some ancient numbers.
![Page 1: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/1.jpg)
Evolution of Numerals
By Evan Evans
![Page 2: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/2.jpg)
Some ancient numbers
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Ancient numbers
![Page 4: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/4.jpg)
Limits of Four
![Page 5: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/5.jpg)
Visual Limits
• Humans have a visual distinguish “limit of four”.
• Different societies came up with ways to deal with this “limit of four”.
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Egyptian 3rd Century BC
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Cretan 1700-1200BC
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England’s “five-barred gate”
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Other Counting Methods
The Elema of New Guinea
Here is a figure to show you what some people have used
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The Elema of
New Guinea
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Counting Sticks
![Page 12: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/12.jpg)
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
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The Greek Numeral System
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Arithmetic with Greek Numeral System
![Page 15: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/15.jpg)
Roman Numerals
1 I 20 XX2 II 25 XXV3 III 29 XIX4 IV (IIII) 50 L5 V 75
LXXV6 VI 100 C10 X 500 D11 XI 1000 M16 XVI
Now try these:
1. XXXVI 36
2. XL40
3. XVII 27
4. DCCLVI 756
5. MCMLXIX 1969
![Page 16: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/16.jpg)
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Roman Addition
MMMDCCCI
CCLXIV
+ DCL
+ MLXXX
+ MDCCCVII
264
+ 650
+ 1080
+ 1807 3801
![Page 18: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/18.jpg)
Roman Subtraction
MMMDCCXXVIII
- MDCCCLII
- MCCXXXI
- CCCCXIIICCXXXII
3728
- 1852
- 1231
- 413232
![Page 19: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/19.jpg)
Roman Multiplication
LXXV
x LMMMDCCL
75
x 503750
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Chronograms
• “Time Writing”
• A sentence or Inscription in which the Capital or Highlighted Letters, interpreted in Roman Numerals, represent a particular date.
![Page 21: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/21.jpg)
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
![Page 22: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/22.jpg)
Chronogram
Activity
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Babylonian Maths
The Babylonians
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Positional Notation
… Hundreds Tens Units
5 7 3
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3600s 60s 1s
BabylonIan
sixties units =64 = 3604
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Numbers Traveled
Through Exploration
Through Trade
Strong Arab Influence
![Page 27: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/27.jpg)
From the Indian sub-continent to Europe via the Arabs
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Roots of 1, 2, 3 and 4
In the WestThe 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
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Based Traced Angles
![Page 30: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/30.jpg)
Which has Evolved into:
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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
![Page 32: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/32.jpg)
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
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Additive Angles Theory
• For each number above 5 you add 1 angle
• Or for a number below 10 you subtract an angle
![Page 34: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/34.jpg)
5 and 10
![Page 35: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/35.jpg)
Additive Angles
5 5 + 1 5 + 1 + 1
6 75
Write line
![Page 36: Evolution of Numerals By Evan Evans. Some ancient numbers.](https://reader031.fdocuments.in/reader031/viewer/2022020102/56649f1b5503460f94c308f4/html5/thumbnails/36.jpg)
Evolution of 5-6-7 in the West
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Evolution of 8-9-10 in the West
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Theory of 5-10
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Evolution in Persia
The numbers evolved differently in Persia
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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
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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
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Rotation of the numerals
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Different dialects
Arabic-Indic ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠ ٩
Eastern Arabic-Indic
(Persian and Urdu) ۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹
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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?
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Evolution of Numerals