Throughout much of the 1600s through the 1800s, Japan was largely isolated from the West. During this time, the Japanese samurai thrived, along with feudalism and the Buddhist religion. A tradition known as Sangaku (roughly translated: Japanese temple geometry) was born in this era. Japanese people from all social and educational classes would work to solve difficult geometry problems and inscribe the solutions on tablets, then hung the tablets on the roofs of Shinto and Buddhist temples as votive. Many of these problems are heavily focused on circles, an uncommon method in the West in the same time period.
These puzzles are reminiscent of two particular games of east-Asian origin that are wildly popular today: Tangrams (China, ~1000 C.E.) and Sudoku (Japan, modern version ~1986 C.E.). Tangrams are obviously similar because of the physical puzzle-like nature. Players are working with physical shapes to make sense of numbers or patterns. The name of the puzzle game Sudoku is reminiscent of Sangaku. Sudoku works strictly with numbers instead of shapes, but the two puzzle games remain similar because they can be customized so many different ways. Sangaku can range in difficulty to be completed by a child or an educated samurai (but one thing that they all had in common was a lack of calculus). Sudoku puzzles become more simple depending on how many squares are filled in at the start.
This above image is an example of a Sangaku. While we could not find a problem to go along with this image, the puzzle would go something like this: given the diameter of the shaded blue circle equals d, what is the area of the shaded orange triangle?
What made Tangrams last through a millennium, while Sangaku are now all but unknown? Are there any other math or puzzle games that are similar to Sangaku? Please leave a comment!
If you’d like to explore the surviving Sangaku, unfortunately a difficult task for anyone who cannot read kanji, find more here or here.