## Saturday, June 8, 2013

### Golden frame

Suppose you bought a painting that the painter did in the Golden ratio of width to height. And you want to find a frame that does it justice. I suggest this:
The painting is the inner square and the frame is the outer. There are some nice things about this choice of frame here's the math:
Little w and h are given by the painting being in the golden ratio, but here the frame is in golden ratio by area, the big width times the big height is exactly the golden ratio times the area of the small frame(w*h*1.618=WH). And nicely that makes the big width almost precisely double the small height. There's sort of an optical illusion going on that the base looks almost 2.5 times the small height but if you measure it is really close to double.
TLDR; The two boxes are in the golden ratio by their lengths to widths and also comparing their areas to each other. And that makes it so the bottom of the big rectangle is almost exactly double the side of the small rectangle.