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THE LEE'S IMPROVED ABACUS
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ADVANCED ABACUS TECHNIQUES
JAPANESE SOROBAN
Fukutaro Kato Techniques: All of Professor Kato's techniques were taught to me by Edvaldo Siqueira of Rio de Janeiro, Brazil. More than anyone Edvaldo has inspired me to continue studying soroban and to investigate more closely the advanced techniques it has to offer.
Professor Kato's method for Pre-determining the Decimal Place in problems of Division & Multiplication
▪ Division
▪ Multiplication
Professor Kato's method for extracting Square Roots
▪ Square Roots
Takashi Kojima Techniques: The following examples come from a book by Takashi Kojima entitled, "Advanced Abacus: Japanese Theory and
Practice"
The Elimination of the Initial Digit of a Multiplier Beginning with One
▪ Elimination
Multiplication by Complementary Numbers
▪ Complementary
Takashi Kojima's method for extracting Square Roots
▪
Square Roots
Fernando Tejón Techniques:
Illustrated here are techniques I've learned from
Fernando Tejón. As a valuable member of the
Yahoo Soroban/Abacus newsgroup, Fernando's
numerous ideas and contributions provide many fascinating insights.
Techniques for multiplication problems having two or more
multipliers
▪
Multifactorial Multiplication
Techniques for using complementary numbers: one technique
simplifies problems
of subtraction; the other solves problems of subtraction where the resulting answer is a negative number.
▪ Complementary
Numbers
Methods for solving problems involving linear
equations.
▪
Linear
Equations
Shane Baggs Techniques: This is an excellent presentation of a very powerful technique for finding the cube root
of a number. Many thanks to Shane for all of his hard work and research and for updating this method
for all of us to use.
▪
Japanese Cube
Root Algorithm
Deji Adegbite Techniques: Thanks to Deji
who's done an
exceptional job in illustrating his techniques for calculating logarithms on a
soroban.
▪
Calculating
Logarithms on a Soroban (along with an
explanation of the technique)
Gary Flom Techniques:
▪ Euclidean norm
of a vector
▪
Abacus Algebra
- techniques for doing algebra on a soroban.
Steve Treadwell Techniques: Many thanks to Steve
for his excellent work on these many wonderful techniques.
▪ Modification to the Crook square root algorithm pdf
▪
Modification to the Crook
cube root algorithm pdf
▪
Balanced ternary arithmetic on the abacus.pdf
▪ Decimal/Binary Conversion on the Soroban.pdf
▪
Multiplication and Division in binary
Hannu Hinkka Techniques: Hannu offers some
wonderful abacus techniques.
▪
Russian
Multiplication - an old technique that requires no multiplication tables.
▪
The Five Bead
Advantage - demonstrating how a 5th earth bead has its advantages.
Joe VanCleave: Many thanks to Joe for
sharing these two fascinating pdf files.
▪
Abacus Tax Calculation Procedure
▪
The Nine Bead Abacus,
it's Theory and Derivation
CHINESE SUAN PAN
The following techniques were taught to me by members of the Soroban/Abacus newsgroup. In particular, I'd like to thank Torsten Reincke whose contributions bring us all to a greater understanding and more thoughtful use of abacus.
Multiplication Techniques
▪ Traditional Multiplication
▪ Modern Multiplication
Division Techniques
▪ Traditional Short
Division
▪ Traditional Long
Division
ABACUS FILES
Anzan (Mental Arithmetic): Two experts share
their thoughts on the Abacus Method of Mental Calculation.
▪
Anzan by Yukio Tani.pdf - from the book
The Magic Calculator - the
way of the abacus
▪
Anzan by Takashi Kojima.pdf - from the book
The Japanese Abacus -
Its Use and Theory
▪
Multiplication - one method that some experts like to use.
▪ Print
Abacus.pdf - Some experts recommend using this aide to help visualize an
abacus. Place the printed abacus on the desk and visualize solving problems.
It's important to actually move the fingers as if doing calculations on a real
abacus.
Explanation of the two kanji characters that make up the word soroban.
Master Craftsman: While the process of making
soroban has become largely mechanical, here are 7 extraordinary YouTube videos
showing a master craftsman hand crafting soroban. The narrator explains the
process in Japanese but the videos need little or no explanation. ▪
Link to
the 7 YouTube videos ▪
CONTRIBUTIONS
The following have been contributed by members of the Yahoo Soroban/Abacus newsgroup. Thanks to Edvaldo, Fernando, Shane & Fabio for sharing these files with us.
League for Soroban Education of Japan
▪ Manual
(60 pages, 8.76 mb PDF File)
▪
Manual in Spanish (12 pages, 477 kb PDF File).
Magazines and Periodicals
▪
The Abacus, in its Historic and
Scientific Aspects
(1.97 mb PDF File) - by Cargill G. Knott, D. Sc. [Edin.], F. R. S. E. [December 16th, 1885]
▪ Retyped version of Knott's
article. Thanks to Nanami Kamimura and Fernando Ota for working to bring us this much easier to
read alternative.
▪ Li (1959) Origins of Chinese Abacus (735 kb PDF File) - appeared in the Journal of the ACM Volume 6, Issue 1, January 1959
▪
Stchoty Le Magasin Pittoresque 1839 p87&88 - two page French language, 19th century article about the Schoty.
Sourced by Fernando Ota. Reference Gallica
(Bibliothèque national de France).
RELATED MATTERS
Various Help pages:
▪ Multiplication and Decimals
▪ Division
Revision
▪ Placing Quotient
numbers
▪ Multiplying
Negative numbers
▪ Learning Basic
Multiplication
▪ Digit Sum Quick Check
- checking answers
▪ The Square Root
of 2 to seven decimal places
▪ Cooking with Soroban
▪ Square
Roots - Welton J. Crook
▪ Find the GCD and LCM of two numbers
▪ Further thoughts on Mechanization
▪ Japanese soroban finger techniques
▪
Magic Number Trick
▪ Cube Roots - Welton J. Crook
▪ Converting
Hexadecimal and base 10
▪ Add &
Subtract Hexadecimal numbers
▪ Predetermine
a Unit Rod (an alternative)
▪ Make a dust cover for your soroban
▪ Fixing a warped frame
▪
Working with Percentages
▪ The
Leap of Faith
▪ Negative
number tutorial (0 - 95 = -95)
The best of the web:
▪ Yahoo Soroban/Abacus
Newsgroup
▪ Abacus, the Art of Calculating
with Beads
▪ Chisenbop Finger
Math
▪ Purchase a Japanese soroban (Tomoe)
▪ Collection of Dr. Jörn Lütjens
▪ The League of Japan Abacus
Associations
▪ Java Applet for leaning Chinese
Suan Pan
▪
Forbes.com ranks abacus 2nd most important tool ever
▪ Soroban Cymru - Soroban in the the U.K
▪ The
Abacus on Wikipedia
▪ Better@Math~Better@Thinking (Soroban, New York City)
▪ Ekimai.com - Abacus techniques with a
link to purchasing soroban in the U.K
▪
Abacus related words in English
▪ Association
Française de Soroban et autres Abaques
▪ Kamedake Abacus Corp, Japan
(makers of fine soroban)
Learning resources:
▪ Stephen Utti's
Soroban Practice Sheets (addition)
▪ Stephen Utti's
Soroban Practice Sheets (multiplication)
▪ Torsten
Reincke's Dictation program
▪ Create your own Practice Sheets (addition,
subtraction, multiplication, division)
▪ solsTiCe d'Hiver's exercise
generator - excellent tool for generating exercises.
▪ An
easy-to-make abacus - make an abacus following these simple instructions.
▪
Brain Scan study - abacus experts versus non-expert groups. (63.8 kb PDF
File)
Dave Bernazzani: Last but by no means least. Dave is the man who got all of this started for me and for so many
others. In 2001 a search of the internet took me to Dave's excellent Soroban/Abacus Handbook. I'd found my
first
teacher. Since switching ISPs in May 2006 Dave's Handbook has been offline. He offers his handbook here in PDF (Adobe Acrobat) format.
▪ Dave Bernazzani's Soroban/Abacus
Handbook (281 kb PDF File)
Dave's Handbook included links to 3 Advanced Operations
▪ Negative Numbers
(107 kb PDF File)
▪ Extracting Square Roots (168 kb PDF File)
▪ Use of Decimals for Multiplication and Division (110 kb PDF File)
Totton Heffelfinger Toronto Ontario Canada
Email
totton[at]idirect[dot]com
