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Do you know that the Japanese have an original mathematics system called Wasan? Young Japanese are seldom aware of this nowadays, because Wasan is a long-forgotten tradition that was substituted for European mathematics in the 19th century. Wasan calculations have unique and colorful names like "Calculation of Cranes and Turtles," "Let's Play Hide and Seek to Decide an Heir" or "How to Weigh an Elephant." Wasan used be actively learned and used as a practical calculation method in the past, but now only old folks nostalgically recall how they learned Wasan quizzes from their parents and grandparents.
In the 6th century when Buddhism was introduced, mathematics also entered Japan from China. In the 14th century, the abacus was also imported from China and spread all over Japan. During the period of national isolation in the Edo Era (1596 to 1868), Japanese mathematics developed on its own through the study of Chinese math. Japanese math developed solely under Chinese influence. (This is quite similar to the situation in Ancient Greece; there, math was based on Egyptian and Mesopotamian math but was not affected by mathematical knowledge in other countries.) In 1600 a book was published on how to use the abacus. This was the advent of the money economy in Japan, when prospering merchants had to be able to calculate their accounts and profits.
Japan continued to develop its own distinctive mathematics systems until, in the 19th century, the Meiji government decided to employ European math for weapons productions and navigation. As a result, few continued to study Wasan and subsequently the traditional Japanese math faded out.
Is Wasan destined to fade out of our memory? Wasan is worthwhile for both adults and children, to exercise and to explore their power of logical thinking. It's fun to try to solve Wasan's story-driven quizzes!

Category Level

Mathematics
History

Editorial Review

Many years ago, when I lived in a European country, I was surprised how often shop clerks made mistakes in counting change. Why, from a country that has produced many world-famous mathematicians? That puzzling experience has haunted me ever since.
Now this book has given me some insight into the problem. The development of Japanese mathematics was deeply rooted in our daily lives. Children were trained by being asked, "Here are 25 candies and there are four of you. How many candies can each of you have if you divide them equally? The child who can calculate right and fastest will get the leftover piece." Children raced to find the right answer. Parents taught their children how to enjoy figures. For Japanese children, applying calculations preceded the study of difficult theories and formulae.
The amusing questions in "Explore the World of Wasan" reflect the actual daily life of the Edo Period. Can you imagine a situation where several burglars are racking their brains over how to divide silk fairly? I was amazed people in those days considered Wasan as entertainment. Japanese mathematics was not only for scholars but for common folk too. I enjoyed this book as a storybook as well as a math text.

Table of contents

• Introduction
• What is "Wasan"?
• Exercise 1: Cranes and Turtles Calculation
• Exercise 2: Divide Oil Equally with Square Cups
• Exercise 3: Yakushi Calculation
• Exercise 4: How Far Do Express Messengers Run?
• Exercise 5: Flower Girls from Kyoto
• Exercise 6: Witty Anecdote of Tycoon Hideyoshi and Sinzaemon Sorori
• Exercise 7: The Discovery of 105
• Exercise 8: How to Cut a Cloth Cleverly
• Exercise 9: Calculations with Mice and Crows
• Exercise 10: How to Weigh an Elephant
• Exercise 11: Silk Burglars' Quandary: How to Distribute Their Loot
• Exercise 12: Let's Play Hide and Seek to Decide an Heir
• Exercise 13: How to Paint a Flag
• Exercise 14: Calculate the Sharing of Bridge Construction Costs
• Exercise 15: The Freight Cost for Shipping Rice
• Wasan Brain Teasers
• Appendix: Sangaku or Math Questions Dedicated to a Shrine (People dedicated a plaque with math questions to a shrine)
• Wasan Today

About the Author

Kenichi Sato was born in Changchun City, Manchukuo (Manchuria / North-eastern China) in1938. He graduated from the Mathematics Division of Tokyo University's Faculty of Science in1962. He taught as the Sub-head of Meiji University's Nakano Hachioji Junior and Senior High Schools and now is a part-time instructor at Kokushikan University.
He is also a researcher in the Education Institution for Private Schools in Japan, president of the Japan Society of Mathematical History, administrative director of the Wasan Institute, and head of the Mathematical Association of Japan (MAJ).