Let us start with a question to the reader, or even two questions. Can you imagine a mathematician who proved a nice theorem, then wrote it down or painted it on a wooden tablet, went with it to a church, or a temple, and hung it there? If you are a teacher of mathematics, can you imagine that you asked some of your students to take their mathematics homework, and carry it to a local shrine? Certainly most of you cannot imagine such practices and, I believe, never heard about such things. However, there is such a country where mathematicians and enthusiasts of mathematics used to carry their best theorems to a shrine, and hung them somewhere on the wall, or under a roof. This practice happened long time ago, and sporadically it happens also today. Such theorems were usually painted on a smooth piece of wooden plank, and sometimes they were even framed. If there was a geometric construction, then quite often the picture was very colorful. Sometimes such a picture contained decorations with flowers, plants, mountains, etc. Some of them were real pieces of art. It was probably a way to thank gods for the moment of enlightenment while solving the problem. 

It is worth to notice that such mathematical tablet contained typically a theorem, its description and usually name of the person who proved it. The proof was usually left with the author. Therefore, such mathematical tablet was a kind of challenge for other people who attended the shrine – “look I proved this, I am a clever person, can you also prove it?” 
The country we are talking about is Japan from the Edo period. The tablets that Japanese enthusiasts of mathematics used to hang in shines were called sangaku, which simply means a mathematical tablet. After the Edo period this custom vanished almost completely, but even now in some temples we can find sangaku from our times. They are, of course, different than those from the Edo period. Also the mathematics on modern sangaku is a bit different from the one developed during the Edo time. The Japanese mathematics from this period was called wasan, and in many aspects it was different from the western mathematics called there yosan.

An old Shinto shrine with sangaku

In order to understand this phenomenon we shall briefly examine history of Japan, and especially beginning of the Edo period. This will give us an idea how mathematics was divided into wasan and yosan. We will also look on the origins of sangaku. Nowadays, in the West, geometry problems displayed on sangaku are often called Japanese temple geometry problems. [Next page]