The Stephenson
Abacus™,
Site Map.
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.
