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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
Professor Fernando Tejón Techniques:
The two chapters in this section illustrate techniques I've learned from Professor Tejón
and from his excellent Spanish language Soroban Manual
Ábaco Japonés Soroban. As a valuable member of the
Soroban/Abacus newsgroup, the Professor's many ideas and contributions provide fascinating insights into his
thoughts on soroban/abacus
technique.
Professor Tejón's techniques for multiplication problems having two or more
multipliers
▪
Multifactorial Multiplication
Professor Tejón's 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
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)
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
Explanation of the two kanji characters that make up the word soroban.
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
(2.8 mb PDF File)
▪
Manual in Spanish (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.
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
▪ 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
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
Learning resources:
▪ Stephen Utti's
Soroban Practice Sheets (addition)
▪ Stephen Utti's
Soroban Practice Sheets (multiplication)
▪ Fernando Tejón's Soroban Pages (in
Spanish)
▪ Torsten
Reincke's Dictation program
▪ Create your own Practice Sheets (addition,
subtraction, multiplication, division)
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
