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Last Update: Wednesday, August 10, 2022
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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
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
Multiplication by Complementary Numbers
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 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
Hexadecimal Arithmetic Octal Code
Octal Hexadecimal Conversion
Decimal Hexadecimal Conversion

Improvements to the Kato Square Root Method
Easy Division

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

Using Hexadecimal Tables - Long Division and Conversion to Decimal
Convert Octal to Hexadecimal - using an Octal Division Table

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

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
Fabrice Bouillerot Techniques: Fabrice shares his very interesting technique for using complementary numbers while solving problems of long division. Merci beaucoup, Fabrice.
Division by Complementary Numbers (DCN)
Dino Marcantonio: Thanks to Dino who has written two excellent tutorials showing us how to turn an abacus into a very powerful inch-foot calculator.
Dino's Foot-Inch Calculator
Multiply & Divide Fractions of an Inch 
masaakimurakami: masaaki shares these wonderfully powerful advanced techniques.
The Other Side of Soroban - A guide to adding, subtracting, multiplying and dividing Negative Numbers
Division with Excessive Quotient

Regressing Multiplier to the power of 10
Multiplication with Excessive multiplicand
masaaki shows us 6 techniques for multiplication - from the 1939 book 'Educating Soroban in Practice' by Gen'ichi Nikai
Two techniques where the divisor begins with One
Division by Complementary Numbers
Specially Crafted Division Tables
Milton Zuluaga: Milton shares a marvelous multiplication technique taught to him by the Cultural Attaché of the Chinese Embassy in Colombia (South América) back in 1996.
Multiply 316 X 29 - this link will take you off site to Goggle Drive
Jesús Cabrera Website, Techniques & Contributions:
Jesús Cabrera, retired (astro)physicist, spent the better part of a year writing two Wikibooks and a 360 page PDF document called 'THE EASTERN ABACUS - A Guide to Bead Arithmetic.' Many thanks to Jesús for these wonderful contributions.
THE EASTERN ABACUS - A Guide to Bead Arithmetic - 360 page pdf file

Using an abacus - a Wikibook
Traditional Abacus and Bead Arithmetic - a Wikibook

Other contrubutions
jccAbacus - New website showcasing some traditional techniques along with a few advanced personal procedures.
A Short Guide to the 5th (lower) bead In this excellent tutorial Jesus shows us how to efficiently make use of the 5th lower bead on a 1:5 bead soroban.

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
Shifting the Unit Rod
Suan Pan and the Unit Rod - Multiplication
Suan Pan and the Unit Rod - 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 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 ▪ 


The following have been contributed by members of the 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).
Spanish Translations
Abacus: el Misterio de la Cuenta (PDF) - Thank you to Carlos Luna for this wonderful Spanish translation.
Multiply 316 X 29 - Carlos Luna

Easy Division - Carlos Luna
Ábaco_Oriental Guía a la Aritmética con Cuentas -Wikilibro - Jesús Cabrera

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 (Bibliothčque 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 Chinese Rule Advantage
Multiplying Hexadecimal Numbers
Multiplying Hexadecimal Numbers using an Octal Table
▪ Convert Hex to Decimal by Dividing by Hex A
Calculating Feet and Inches - base 12 & an inverted suan pan
Adding Hexadecimal numbers using the Binary number system
The best of the web:
Soroban/Abacus Newsgroup
Purchase a Japanese soroban (Tomoe)
The League of Japan Abacus Associations
Java Applet for leaning Chinese Suan Pan
The Abacus on Wikipedia
Better@Math~Better@Thinking (Soroban, New York City) - Abacus techniques with a link to purchasing soroban in the U.K
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)
Akademia sorobanu - Soroban Academy (in Polish)
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




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