A sangaku is a picture used to represent a mathematical theorem.

The idea is that you only get a picture and then formulate your own conjecture to it, which you can then prove.

Which famous theorem will this be anyway?

 

Click on the spoiler for some mathematical explanation, if you wish ;)

Spoiler

If you look at the two squares (the grey border is there for decoration, so only the inside), you can see that they are the same size.

If I then look further at the overall picture, it turns out that the area of the large inner square (in the left-hand picture) is the same size as the area of the two squares in the right-hand picture.
It is easy to see that this is correct. The inner squares are the same size and there are four right-angled triangles of the same size inside them, so the rest of the area is exactly the same.

So far, so little complicated maths.

You calculate the area of a square by taking the square of the side length. And now it gets even better.
If we first look at the picture on the right, we can see that the small square lies exactly on the short side of the rectangle, so the area of this square is the square of the small side of the rectangle.
The large square in the right-hand picture lies on the long rectangular side, so the area of the large square is the square of the long rectangular side.

Now let's take a look at the left-hand picture. There, the square lies on the diagonal, the longest side of the triangle. The area of the left-hand square is therefore equal to the square of the longest side of the triangle.

As we have just proved that the area of the squares in both pictures is the same, it is clear that the square of the short rectangular side plus the square of the long rectangular side equals the square of the longest side.

If we now denote the length of the short rectangular side as a, the length of the long rectangular side as b and the length of the longest side of the triangle as c, we get
a^2 + b^2 = c^2
 

And that's the famous Pythagoras' theorem

 

Edited April 25, 2024Apr 25 by KlaasK

Nice idea.

I remember drawing figures similar to that in Maths class!