Traditional Abacus and Bead Arithmetic

This textbook is an introduction to the Traditional Beads Arithmetic (珠算; zhūsuàn in Chinese, shuzan in Japanese), or the use of the eastern fixed-bead abacus (算盤, suanpan in Chinese, soroban in Japanese) as practiced in China, Japan, Korea, Vietnam, etc. for at least four centuries.

孤雁歸隊 (Gūyàn guīduì) The lone geese return to flock. Allegory of a traditional division exercise with abacus (998001/999)

Traditional Chinese abacus illustrating the suspended bead use

Chinese beads arithmetic has been inscribed in 2013 on the UNESCO Representative List of the Intangible Cultural Heritage of Humanity, however, the information available in English on this subject is scant and scattered, so it is worth the effort of trying to gather it somewhere, for instance, in this book.

This text is aimed at those who already have a basic level in the use of the abacus following the Modern Method currently taught and who wish to delve into the history of their favorite instrument and mathematics in the Far East. After studying this text and practicing its content, the reader should be able to perform calculations according to the Traditional Method using any type of eastern abacus and understand (whenever possible) why they were done that way.

Table of content

• Introduction
• Addition and subtraction
  • Use of the 5th lower bead
  • Extending the 123456789 exercise
• Division
  • Modern and traditional division; close relatives
  • Guide to traditional division (帰除法)
  • Learning the division table
  • Dealing with overflow
  • Traditional division examples
  • Special division tables
  • Division by powers of two
• Multiplication
• Roots
  • Square root
  • Cube root
• Appendix: Abbreviated operations
• Bibliography

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• Contributors
• Resources for contributors