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**by Steve Stephenson**

Revised April 24, 2008 (copyright)

Introduction (The Third Paper)

- Capabilities
- Potential Modern Uses
- Historical Inspirations
- Roman Numeral Subtraction
- Structure (Exponential Numbers with Digits in Subtractive Form)
- Counting
- Adding a List of Multiple-Digit Base-10 Numbers with Mixed Signs

Ancient Scientific Calculators (The First Paper)

- Multiplication of Base-10 Numbers
- Readable Digits
- Pebble / Counter Efficiency (How to minimize the number of counters needed.)
- Early Thoughts: Archimedes, Salamis Tablet
- Historic Clues

Base-60 Multiplication Example

- Partial products too numerous to do problem without an abacus.

An Ancient Base-60 Calculator? (The Second Paper)

- Structure of Base 60 Counting Boards
- Operations on Base 60 Counting Boards
- Representing Digits as Sums of Five, Ten, Three, or Six Complements
- Yale Tablet YBC 7289 Calculation of sqrt(2)/2
- Analysis of Partial Product Problem When Using a Multiplication Table Instead of an Abacus

References with Quotes and Notes. Some of the interesting stuff here is:

- Kojima's argument that Roman Hand Abacus is progenitor of all non-American constrainted bead abaci, esp. the Chinese suan-pan and the Japanese soroban.
- Frontius' pipe calculations in The Aquaducts of Rome could not have been done on a Roman Hand Abacus. Frontius must have used a full featured counting-board style abacus.
- Herodotos' calculation errors duplicated on The Stephenson Abacus™.
- Correct and incorrect Babylonian sexagesimal products duplicated on The Stephenson Abacus™.
- Sexagesimal usage in ancient Egypt.
- Friberg's timeline for the early origins and development of math.

Tools

- A paper counting-board template. Cut-and-paste three to make each Stephenson Abacus™counting-board, use three counting-boards for multiplication or division. Use pennies as counters.
- Excel workbook models of Stephenson Abacus™counting-boards.

©
2006-2008 Stephen Kent Stephenson. Some
Rights
Reserved.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

sks23cu AT gmail

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

sks23cu AT gmail