Edo Period Math Tablets Still Hold Right Formula To Baffle, Impress Viewers

Edo Period math tablets still hold right formula to baffle, impress viewersWhen students from a U.S. college came to Japan on a two-week tour, they couldn't help but be in awe as they visited Myojorinji temple here.
The 11 students from Randolph-Macon College in Ashland, Va., were moved to shout such words of praise as "beautiful" at the temple, which stands near the top of Mount Kinshozan.

Their amazement came at seeing a traditional tablet bearing colorfully illustrated geometry problems dating to the Edo Period (1603-1867), known as "sangaku."

On their visit in January, they glimpsed a wooden board bearing triangles, squares, circles and other geometric figures colored blue, red, white, yellow and other various hues that hangs from above the sliding doors at a living room for monks.

Measuring 57 centimeters by 224 cm, the wooden plate includes 12 geometric questions, which are written in kanji characters.

The purpose of the visit by the U.S. students to Japan was to see the sangaku offered to shrines and temples by feudal-era scholars of “wasan” traditional mathematics.

David Clark, 35, an associate professor of mathematics at the university, told his students that the wooden tablet is what they came to see.

The 11 students were engaged in a one-month intensive course on Japanese culture, and were to spend two weeks touring Tokyo, Kyoto and elsewhere in Japan. But the main theme of the program was studying Japan’s traditional mathematics.

According to Myojorinji, the sangaku tablet was dedicated to the temple in 1865--in the closing days of the Tokugawa Shogunate--by 27 students of Asano Takamitsu, a wasan mathematician who ran a private school here.

“Sangaku were generally presented by mathematicians to show appreciation for the fact they were able to solve difficult wasan problems,” said Hidetoshi Fukagawa, a 71-year-old researcher of sangaku who works as a part-time lecturer at Kogakkan University and served as a guide to the U.S. students. “Sangaku also offered entertainment for farmers, merchants and other ordinary people of the time.”

The group of students then went to Tashirojinja shrine in Yoro, also in Gifu Prefecture, to view sangaku owned by the shrine.

One of the college students, Steven Lohrey, 21, whose major is physics, succeeded in solving a question written on a sangaku tablet there. The senior high school-level problem requires people to find the diameters of four circles in a square.

After being told the question was created by a 13-year-old boy named Iguchi Momoichiro, Lohrey praised the Edo culture that allowed such a young student to become so familiarized with mathematics.

Wasan developed based on Chinese mathematics. As wasan came to be studied by many people--it is believed that there were more than 80,000 private schools of the traditional math throughout the country in the late Edo Period--the scholars established unique Japanese-style mathematics on their own.

While geometrical figures on sangaku are typically painted in bright, eye-catching colors, it is said that wasan teachers used the aesthetic appeal of the wooden panels to attract more students to their schools.

More than a century after the end of the Edo Period, high quality problems posed on sangaku tablets are now drawing attention from across the world.

Wasan mathematician Seki Takakazu (c. 1640-1708) is said to have established the world’s first solution to simultaneous equations using a determinant.

A problem in a sangaku dedicated in 1822 to Samukawajinja shrine in Kanagawa Prefecture proves the famed Soddy's hexlet theorem more than a century before British chemist Frederick Soddy, who won the Nobel Prize for his discovery of isotopes, released the theory in 1936.

Fukagawa, a former high school teacher in Aichi Prefecture, was won over by sangaku in his 20s and has since conducted surveys on the academic offerings. According to Fukagawa, 900 sangaku tablets remained in existence across Japan as of 2005.

He has also been working with researchers overseas to promote attractions of the traditional wooden tablets. Fukagawa in 2008 co-authored a book titled “Sacred Mathematics: Japanese Temple Geometry” with Tony Rothman, a physics professor at Princeton University.

Fukagawa said he started accepting requests from aboard to see existing sangaku after the book was published. Last summer, he toured Atsutajingu shrine in Nagoya with 10 high school students from Singapore.

According to Fukagawa, a Turkish researcher will visit Japan to study sangaku in May. He has to date guided experts from Germany, New Zealand, Switzerland, Denmark and elsewhere in the world.

In early February, Fukagawa received an e-mail from the Randolph-Macon students telling him that they created a sangaku of their own and were displaying it in the college’s library.

“That may be the world’s first sangaku created at the hands of people overseas,” said Fukagawa. “I will be happy if more people around the globe become interested in sangaku.”