The Evolution of Our Number System

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• Demonstrate an understanding of the evolution of
  our numeration system by connecting concepts such
  as, counting, grouping and place values from the
  past to the present
• Recognize early systems of numeration
• Write numbers in Roman, Babylonian, Greek and
  Egyptian

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• The Very Beginning
• Ancient Egypt
• Ancient Greece
• Roman Empire
• Babylonian Numeration
• The Mayans
• Hindu-Arabic Numerals
• Brief History of Zero
• Timeline

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D
E
C
B
G
F
A
A. African B. Egyptian C. Babylonian D.
Greek E. Roman F. Mayan G. Hindu-Arabic
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• First known form of counting
• Used grouping
• Ishango Bone c. 18,000 BC

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Ishango Region
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• Developed in
• 3400 B.C.
• Grouping by 10s
• Additive system
• Disadvantages
• Examples
• 24
• 124
• 1240

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• Write the following numbers
• 672
• 42,320
• 345
• 567,922

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• Rhind Papyrus, c. 1650 BC

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• Moscow Papyrus, c. 1850 BC

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• Ciphered numeration system
• 3000 B.C.
• Disadvantages
• Examples
• 24
• 124
• 1240

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• Write the following numbers
• 672
• 188
• 345
• 949
• 888
• Convert to our number system
• ???

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• Zenon Papyri, c. 200 AD

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• 500 B.C. 100 A.D.
• Grouping , additivity
• and subtraction
• Positional
• Disadvantages
• Examples
• 24
• 124
• 1240

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• Write the following
• numbers
• 672
• 24
• 1098
• 777
• 479
• 1776
• Your birth year

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• Convert to our present
• system
• XL
• MDCXII
• MCMLXIV

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D
E
C
B
G
F
A
A. African B. Egyptian C. Babylonian D.
Greek E. Roman F. Mayan G. Hindu-Arabic
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Maximum Extent of the Babylonian Empire, c. 1750
BC
Maximum Extent of the Egyptian Empire, c. 1500 BC
Maximum Extent of the Roman Empire, c. 15 AD
Homeland Colonies of Greek Civilization, c. 700
BC
Maximum Extent of the Roman Empire, c. 100 AD
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• 3000 - 200 B.C.
• Positional system
• Place Values
• Base of 60
• No place holder
• Disadvantages
• Examples Write the following numbers
• 24 48
• 124 672
• 1240 3702
• Convert to our number system

V
lt
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• Bablyonian Tablets, c. 1800 BC

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• Bablyonian Tablets, c. 1800 BC

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• 300 900 A.D.
• Place value system
• Base 20
• Introduced zero

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• Mayan Codices

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• 800 A.D.
• 10 symbols
• Grouping by tens
• Place value
• Additive and multiplicative

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• Who discovered it? Why?
• Place holder (space, , ? )
• A number itself (7th century India)
• the sum of zero and a number is the number
• zero subtracted from a number is the number
• zero multiplied by a number is zero
• zero divided by a number is zero
• a number divided by zero is
• Zero divide by zero is .

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• 3000 BC Egyptian Numerals
• 2000 BC Babylonian (Iran/Iraq)
• 400 BC Greek Ciphered Numerals
• 100 BC 500 AD Roman Empire
• 300 BC Mayan (Central America)
• 500 AD Hindu Numerals
• 800 AD Arabs adopt Hindu Numerals
• 500 1100 Dark Ages in Europe
• 1202 Fibonacci publishes Liber Abaci

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• Which numeration system do you think works best?
  Why?
• How important is zero in our Hindu Arabic System?
• Do you think our numeration system will continue
  to evolve?