## 23.4.12

### Silver ratio windows

I was recently at Jyväskylä University in Finland and saw these windows on the Agora building. They looked like silver rectangles to me, so I snapped a picture to measure. Sure enough, nearly exactly by my measurements on the image.

The silver ratio, by the way, is 1+√2 : 1. It has many connections to the golden ratio. It's equal to 2+1/(2+1/(2+1/(2+1/(2+... (Replace all of those 2s in the fraction with 1s and you get the golden ratio).

If you add a unit square to a 1:√2 rectangle (A4 paper, for example) you get a silver rectangle. If you subtract a unit square from a 1:√2 rectangle you also get a silver rectangle.

A4 rectangle plus a unit square is silver:
A4 rectangle minus a unit square is also silver:

And just like you can remove a series of squares infinitely from a golden rectangle, you can remove a series of 2 squares infinitely from a silver rectangle...

There's lots of other cool properties... I've been fascinated with these "precious metal ratios" lately (gold, silver and yes bronze and others!) so it was exciting to spot these silver ratio windows. I hope this was an instance of intentional mathematics!