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

• 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    

2 over 5: Earlier Roman, Chinese        

1 over 4: Later Japanese

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