ADVANCED ABACUS TECHNIQUES
JAPANESE SOROBAN & CHINESE SUAN PAN
What's new on these pages
Last Update: Wednesday, August 10, 2022
THE LEE'S IMPROVED ABACUS
The Lee's Abacus - a Demonstration
ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual
▪ Site Map
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
▪ 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.
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.
▪ Traditional Multiplication
▪ Modern Multiplication
▪ Traditional Short Division
▪ Traditional Long Division
Shifting the Unit Rod
▪ Suan Pan and the Unit Rod - Multiplication
▪ Suan Pan and the Unit Rod - Division
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).
▪ 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.
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)
▪ Ekimai.com - Abacus techniques with a link to purchasing soroban in the U.K
▪ Kamedake Abacus Corp, Japan (makers of fine soroban)
▪ 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