ADVANCED ABACUS TECHNIQUES
JAPANESE SOROBAN & CHINESE SUAN PAN

What's new on these pages
Last Update: (Wednesday January 29)
THE LEE'S IMPROVED ABACUS
The Lee's Abacus - a Demonstration
ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual
Site Map

tiny soroban gif  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 Tejˇn Techniques: Illustrated here are techniques I've learned from Fernando Tejˇn. 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
Octal Arithmetic on the Soroban

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.
Binary Method for Calculating GCD - an alternative to an earlier tutorial

Joe VanCleave:  Thank you to Joe for sharing these two fascinating pdf files.
Abacus Tax Calculation Procedure
The Nine Bead Abacus, it's Theory and Derivation

 
Marcos Labriola Techniques: Marcos kindly shares these powerful techniques that illustrate how easy it is to alternate between Decimal, Binary and Octal number systems. Thank you Marcos.
Conversion from Decimal to Binary

Decimal & Octal Conversion Techniques
 

small abacus gif 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
 

small abacus gif 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.
25 anzan addition subtract  exercises with answers ( 340 kb .zip file)

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 place your fingers onto the printed abacus and move them 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] Thanks to Nanami Kamimura and Fernando Ota.
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 (BibliothŔque national de France).
Early Calculation (5.61 mb PDF File) - off site link to very interesting 56 page article featuring many early calculating methods and devices. Thanks to both Ed Thelen and Michael R. Williams.
 

small abacus giftiny soroban gif 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)
Shifting the Unit Rod
Chinese Division Rules on a Soroban
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. J÷rn LŘtjens
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
Abacus related words in English
Association Franšaise 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

 

 

 

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