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comment by mike
mike  ·  2201 days ago  ·  link  ·    ·  parent  ·  post: What are you working on today?

I bought a viking camp 6 months ago and have been converting it to a math creativity center. We'll be opening in 2 months and there is still too much to do! I've just finished putting up the trim in the big banquet hall. It was a dark viking-y room with stone and rough wood and runes carved everywhere. Now it is light and bright and ready for artwork.

I'm eager to begin on the doors. There's 3 in the room. One of them is almost exactly the silver ratio -- you've heard of the golden ratio? It's the first in a family of interesting ratios. I'll write a post about if anyone's interested. With a golden rectangle you can cut off a square and the part that's left is another golden rectangle, so you can keep cutting infinitely. With a silver rectangle, you can cut off 2 squares and be left with a silver rectangle. The ratio is 1:(sqrt(2) + 1). Amazingly, one door is very nearly in the bronze ratio (you can cut off 3 squares). And the third is close to the the golden ratio + 1.

So I want to use these ratios in designs on all of the doors. Here's some sketches:

The first is golden ratio + 1, the second is the silver ratio, and the third is the bronze ratio (which I don't have a really good idea for yet). I was really happy with the arrangement of squares and half-circles on the silver ratio door – and then afterwards found that someone else of course has already discovered this design.

So that's what I'm up to this week!

MisterMentat  ·  2201 days ago  ·  link  ·  

Please write about those ratios.