VEDIC MATHEMATICS : Abstraction

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VEDIC MATHEMATICS Abstraction

• T. K. Prasad
• http//www.cs.wright.edu/tkprasad

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Numbers Representation and Operations
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What are numbers?
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Numbers as Abstraction
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More on Abstractions
Fruits
Planes
Fighter Planes
Vegetables
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Mathematics

• Mathematics deals with abstraction of our
  understanding about the world.

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Abstraction Another Example

• Five little monkeys jumping on the bed.
• One fell down and broke its crown (head).
• How many monkeys will now jump on the bed?
• 5 1 4

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Numbers vs Numerals
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Symbols for numbers Egyptian Numerals
Hieroglyphs 3500 BC
10
                                                
                                                
                                        12,425
birds
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Symbols for numbers Roman Numerals

• Alphabet I, V, X, L, C, D, M,
• Numerals
• I, II, III, IV, V, VI, VII, VIII, IX, X
• 1, 2, 3, 4, 5, 6, 7, 8,
  9, 10
• XI, XII, XIII, XIV, XV, XVI, XVII, XVIII,
  XIX, XX
• 11, 12, 13, 14, 15, 16, 17,
  18, 19, 20
• L, C, D, M, LXIII, XL,
  MCMLXIX
• 50, 100, 500, 1000, 63, 40,
  1969

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(contd)

• XIX
• Is this 11 10 21? Or, is this 10 9 19?
• 19
• If smaller digit follows larger digit, the digits
  are added. If the smaller digit precedes larger,
  the smaller is subtracted from the larger.
• More examples of disambiguation
• XCIX 99, but IC and ILL are disallowed.
• CLXXXIX 189, but CIXC is disallowed.
• MCMXCIX 1999, but IMM and MIM are disallowed.

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Summary Two Lessons

• Fixed Alphabet for numerals Use a fixed set of
  symbols to represent all numbers.
• Unambiguous representation for number Each
  numeral must have a unique meaning (that is, a
  unique number associated with it).