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## Monday, February 16, 2009

### Heptagonal Flower Twist

Heptagonal Flower Twist, by Andrew Hudson

Our 7th week already! This week we've got something a little unusual for you-- but it'll take some work of your own to get the full potential out of this diagram. It looks like a diagram for a single model, but in fact I've given you the tools to create any regular polygon from a rectangular sheet of paper, by applying the Fujimoto approximation to angles instead of line segments.

So without further ado, here are the diagrams:
http://dl.getdropbox.com/u/232756/heptagon.pdf

1. It would be helpful, for the mathematically lazy (like me) to tell us what angle one is estimating in step 2. Not mind you, that most folks (myself included) can estimate to that much accuracy, but it's good to know a ballpark, anyway.

It's 77-ish degrees from the horizontal edge, or 13-ish degrees from the vertical, isn't it?

(Actually it's kind of a cool number:

77.142857142857142857142857142857...

if I'm figuring it correctly. Do let me know if not!)

2. You should be estimating 3/7 of 180 degrees-- so yeah, 77 degrees is as close as you'll get without tools...

But the beautiful thing is, it really doesn't matter where you estimate; after two rounds of steps 3-5 the error will be reduced to 1/64, which is less than a degree of error as long as you stay in the right quadrant.