30+ Centuries of Computation in a 21st-Century Format



      Pre Session Warm Up Activities & Questions

1. What's the scientific name for "fools' gold?"
2. What's a shekel?
3. For what is Napier famous?
4. Explain the "Eye of Horus."
5. How did Archimedes die?
6. Write 2510 in base 2.
7. Simplify: log(2) + log(3).
8. Introduce yourself to those around you and discuss your answers.

    History    

This lecture version is page mathnstuff.com/papers/matyc10.htm.
The essay version is page mathnstuff.com/papers/amtnj09.htm.




























Disclaimer

      This is the "Azzolino Version" of math history based on:

  • research in computing devises, math history, and linguistics,
  • extensive expertise with manipulatives.

      It is left for you to determine the "truth."

                        -- Agnes (A≤) Azzolino

    History    
































Contents

  • Origin of Numbers -- Named and Unnamed
  • Talley Sticks
  • Tokens & Coins
  • Writing Numerals
  • Egyptian Multiplication
  • Abaxes (Sand Table), Reckoning Boards, Banks
  • Abacuses
  • Napier's Bones
  • Slide Rules
  • End Notes
  • Debrief
        History    






























Origins -- Named and Unnamed
Unity, Duality, Multiplicity

    unity -- only one
    The King
    The Queen
    duality -- exactly two
    pair of sox
    yoke of oxen
    multiplicity -- Collective Nouns   
    herd of antelope
    colony of ants
    swarm of ants
    army of ants
    culture of bacteria
    crowd of people
    herd of zebras
    zeal of zebras
   
    History    
































Tally Sticks

    History   Text    

































    History    

































    History    

































    History    

































    History    

































    History    

































    History    

































    History    

































    History    

































    History    
































    History    

































    History    

































    History    

































    History    
































Tokens Then Coins

    Hands Coins History LA  
































Writing Numerals

    No. System   Hyro   History   LA    
































Egyptian Multiplication

Multiply 45671 by 92.
    1st 2nd 3rd 4th Resource Page History   Board LA  
































Abaxes (Sand Tables), Reckoning Boards, Banks

    Board History   LA  
































Abacus

2 over 5: Earlier Roman, Chinese        

1 over 4: Later Japanese

    History   LA  
































Napier's Bones

    Resource History   N Bones LA  
































Slide Rules

    History   Slide LA  
































End Notes

    Sources History    
































Debrief


Origin of Numbers -- Named and Unnamed

  • Numbers started out as part of names - yoke of oxen, herd of cattle, gaggle of geese.
  • Days of conch shells and taboos about counting.

Talley Sticks

  • Though conventional wisdom for years said otherwise, "primative people" did count more specifically than "many."
  • The Ishago Bone possibly of 20KYA, 20 thousand years ago, with primes 11, 13, 17, and 19 marked, and a crystal.
  • 35,000 BCE to 8,500 BCE -- Talley marks made permanent and important math records.

Tokens Then Coins

  • 10,000 BCE to 6,000 BCE -- Tokens served as movable and permanent records.
  • The use of tokens set the stage for the earliest writing.
  • 3000 BCE - Shekels, temple coins, were used in Sumeria.
  • 600 BCE -- Minted staters were used in Lydia (Turkey) and the use of coins spread quickly there after.

Writing Numerals

  • ADDITIVE SYSTEM, Egyptian, Greek [8], early Roman
    - The order of the "symbols" doesn't matter though they are often ordered.
  • MULTIPLICATIVE SYSTEM, Chinese, as in modern expanded notation
    - Write from largest to smallest a string of pairs of "number of" then "value of symbols" to write the number.
  • POSITIONAL SYSTEM, decimal, Greek & Roman Numerals
    - Order or position does matter.

Egyptian Multiplication

  • Eye of Horus and a memory trigger for the power series that facilitated multiplication and division.
  • Used for division and multiplication and still used in Middle Ages as duplation and mediation.
  • FIRST! statisticians and secretive about their work.

Abaxes (Sand Table), Reckoning Boards, Banks

  • Sand Tables, or beaches, for drawing accurate, measurable scale drawings.
  • Reckoning Boards, from the Egyptian, thorugh the Banks, merchant benches (as in bank rupt, bankrupt) of the Middle Ages.
  • With calculi, pebbles, to compute.
  • With choice of lines or spaces or both or vertical or horizonal orientation with whatever base is needed -- guilder, pound, or shekel.
  • Set the stage for the Roman hand-held abacus and other abacuses.

Abacuses

  • First hand-held calculators.
  • Great for speed, portability, shakey tables and tax assesors -- think how easy a tith is to compute on a board or abacus.

Napier's Bones

  • MAJOR COMPUTING ACHIEVEMENT! especially for division!
  • Can you SEE the inspiration for log computation?

Slide Rules

  • Take John Napier's natural log work and add the scales of Edmund Gunter and William Oughtred's paired Gunter scales and computation may be completed ala the sand table and scale drawing.
        History    





























Contents

    History  
[MC,i. Home] [Table] [Words] Classes [this semester's schedule w/links] [Good Stuff -- free & valuable resources] spread sheet notes
© 2010, Agnes Azzolino
www.mathnstuff.com/papers/matyc10.htm