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VEDIC MATHEMATICS : Abstraction

VEDIC MATHEMATICS : Abstraction. T. K. Prasad http://www.cs.wright.edu/~tkprasad. Numbers : Representation and Operations. What are numbers?. Numbers as Abstraction. More on Abstractions. Fruits. Planes. Fighter Planes. Vegetables. Mathematics.

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VEDIC MATHEMATICS : Abstraction

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  1. VEDIC MATHEMATICS : Abstraction T. K. Prasad http://www.cs.wright.edu/~tkprasad Abstraction

  2. Numbers : Representation and Operations Abstraction

  3. What are numbers? Abstraction

  4. Numbers as Abstraction Abstraction

  5. More on Abstractions Fruits Planes Fighter Planes Vegetables Abstraction

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

  7. 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 Abstraction

  8. Numbers vs Numerals Abstraction

  9. Symbols for numbers : Egyptian Numerals Hieroglyphs : 3500 BC Abstraction

  10. = 12,425 birds Abstraction

  11. 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 Abstraction

  12. (cont’d) • 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. Abstraction

  13. 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). Abstraction

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