Japanese ‘sangaku’ paintings reveal the sacred side of maths
This image is a stunning example of one of the most intriguing practices in the history of mathematics. Between the seventeenth and nineteenth centuries, the Japanese used to hang up pictures of maths theorems at their shrines.
Called “sangaku”, the pictures were both religious offerings and public announcements of the latest discoveries.
It’s a little like as if Isaac Newton had decided to hang up his monographs at the local church instead of publishing them in books. More than 700 sangaku are known to have survived, and the above shape is a detail from the oldest one that exists in its complete form.
The painting dates from 1686 and hangs in the Kitano Tenman-gu shrine in Kyoto, which I visited recently. During the seventeenth century, when mathematics was transformed in the West by scientists like Newton, Japan was completely isolated from the rest of the world and it developed its own mathematical traditions - discovering many famous theorems independently.
The eleven shapes on the sangaku I saw (pictured below) contained circles, triangles and squares, familiar shapes but stylistically quite different to diagrams in Western geometry books of that period.
The purpose of a sangaku was threefold: to show off mathematical accomplishment, to thank Buddha and to pray for more mathematical knowledge. Sangakus usually don’t provide a proof of the theorem, and though books of them have been published in Japan for many years, some theorems are still unsolved.
There was writing underneath the images of the sangaku I saw although I could not source a translation.
If you want to find out more, the 2008 book Sacred Mathematics by Tony Rothman and Fukagawa Hidetoshi presents a history of sangaku and explains the maths behind almost 200 problems. Here are 20 examples online.