Comments on: How to Make a Pentagon from a Circle

By: darren

darren — Sun, 07 Jan 2007 06:14:33 +0000

There is a sequence for folding a pentagon from a square, which may be handy for some. If folded perfectly, you get a mathematically accurate pentagon at the end. Irregularities of folding something real, by a human folder, will give you results more or less accurate. The diagram can be found here.

By: oschene

oschene — Sun, 26 Nov 2006 04:37:41 +0000

Thus, I am answered. (It never hurts to have a mathematician dropping by.) That does sound easier and I certainly will give it a try.

I was trying to imagine teaching that rose today – there are a lot of stumbling blocks to get over, though I know people would enjoy collapsing the spiral. Perhaps at the next Convention.

By: Tom Hull

Tom Hull — Sun, 26 Nov 2006 03:02:30 +0000

Hey there! Nice rose, and yes, pentagons are fun. But if I had to teach such a pentagon to a group of people (say, for your rose), I’d opt to use the Fujimoto angle approximation method to divide 360 degrees into 5 equal (or close-enough-for-all-practical-purposes) parts. Do you know this? It works exactly like his method for approximating 1/5ths from a strip of paper, but you do it for angles. So you start with one crease from the center to the side (a radius of the circle) and call this the 0 degree crease. Then guess where the 72 degree crease would be, perhaps by making a pinch on the circle’s border. Then you have two “angles” in the circle — one approx 72 deg and one approx 360-72 = 288 deg. Divide the 288 deg angle in half with another pinch on the border of the circle. This makes a pinch at roughly the 72 + 288/2 = 216 deg mark, except now the error you had has been divided in half. Then bring the 216 deg pinch and the 0 deg mark together to get a pinch for approx the 288 deg mark. Then work your way around the other way of the circle — in the end you’ll have a much better approximation of the 72 deg pinch (your initial error will have been divided into 16ths — barely visible!).

Maybe it’s me, but I find that a lot easier and kinda fun.

By: oschene

oschene — Fri, 24 Nov 2006 16:38:06 +0000

Complex, sirrah! I think your Swiss Army knife is perhaps missing the Ockham’s Razor blade.

Find me a method with fewer than eight steps to elegance. I will wait.

*cough*

By: Eric Gjerde

Eric Gjerde — Fri, 24 Nov 2006 15:12:26 +0000

Wow, that seems like a really complex way to build a pentagon. But indeed, it is elegant. I love geometry done with compass and straightedge, it feels “right”… much less insulting to the paper muse than plotting angles in Illustrator.

My opinion, anyhow!