VEDIC MATHEMATICS : Positional Number System

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VEDIC MATHEMATICS Positional Number System

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

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Symbols for numbers Hindu Arabic System
1 11 12 13 14 15 16 17 18 19 2
1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1
8 1 9 1 1
1 11 12 13 14 15 16 17 18 19 2
1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1
8 1 9 1 1
1 2 3 4 5 6 7 8 9 1
Read as blank.
Need care when writing (aligning) numbers with
blanks.
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Invention of Zero
Attributed to Indian Mathematicians. In fact,
zero thrust itself upon us in the context of
positional number system!

• 1,2,3,4,5,6,7,8,9
• 1 ,11,12,
• ..
• 1 , 1 1, 1 2,

• 0,1,2,3,4,5,6,7,8,9
• 10,11,12,
• ..
• 100, 101, 102,

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Names of Zero
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Vedic Mathematics

• Vedas Texts from Ancient India in Sanskrit
• Mathematics Study of quantity (how much?),
  change (how fast? ), space (shapes),
• Vedic Mathematics is the mathematical knowledge
  of ancient Hindus passed down through generations
  (initially verbally and later codified) as slokas
  (verses) in Sanskrit.

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Invention vs Discovery

• Discovery is finding out what exists but
  previously unknown
• Discovery of America by Christopher Columbus (of
  Spain) in October 1492
• Discovery of Helium by Sir William Ramsay
• Ref Sun, Balloon
• Discovery of Galaxies by Edwin P. Hubble
• Number zero was discovered.

• Invention is something you create out of
  imagination
• Invention of Car
• Invention of Wheel
• Invention of Computers
• Invention of Television
• Symbol zero was invented.

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Why base 10?

• 10 fingers, 10 toes, ?
• Alternatives
• Base 60 (Babylonian Cunieform)
• Upto 59 by crescent (weight 10) and wedge (weight
  1)
• "
• "
• 1 hour 60 minutes, 1 minute 60 seconds,
• 1 year 360 days, 1 day 24 hours
• 24 1 x 2 x 3 x 4 60 1 x 2 x 3 x 2 x 5
• Base 2 (Modern)
• Two eyes, two ears, two hands, two legs, ?
• Digital Computers based on switches 0, 1

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Dashavtar

• Matsya (fish),
• Kurma (tortoise),
• Varaha (boar),
• Narasimha (man-lion),
• Vamana (dwarf man),
• Parashuram
• Ram (moral man),
• Krishna (philosophical / practical man)
• Balaram
• Kalki

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Symbols for numbers Hindi (Devanagari) Numerals
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Representing Numbers Positional System

• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• For larger numbers
• Problem cannot keep inventing new symbols
• Solution use finite number of symbols with
  Position-based Weighting
• 52 5 10 2
• 743 7 100 4 10 3

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Positions and Weights
43210 4 10,000 3 1,000 2 100 1
10 0
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Exercises

• 1a) Local Values
• 1b-e) Verbalizing Numbers

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Large Numbers

• Hard Disk Storage in 30 GB IPod
• 30 x 1024 x 1024 x 1024 bytes (30 Giga bytes)
• 32,212,254,720 bytes
• Number of stars in our Milky Way Galaxy
• About 100,000,000,000 (100 billion)
• Googol
• One followed by 100 zeros
• Googolplex
• One followed by Googol zeros