I've been fiddling...

[capri0mni]

... Making cut paper, five-pointed, stars from squares of paper.

Five folds, one straight cut. A video is here: https://youtu.be/iraWBwcOfU8 (haven't found a text, or diagram, or still picture, set of instructions yet). It really is ingenious. I wondered who figured out the math, 'cause drawing a pentagram by Euclid's method, using straight edge and compass, is mind-numbingly complicated.

Comments

[spiralsheep]

I love that sort of instructional vid. It's what t'interwebz does well. Thank you for the link.

[capri0mni]

Yeah. Me too. You don't even need audio, or to understand the language. You just watch how it's done.

And you're welcome!

[pebblerocker]

That's so clever! Thank you!

I know how to make a pentagon by tying a strip of paper in a knot. A simple knot comes out five-sided when tied in something flat. But how to fold a five-pointed star seemed impossible until I saw it done.

[capri0mni]

I'm reminded of this video, from the YouTube channel "Numberphile," about how you can perfectly trisect an angle with origami, while it's impossible with Euclid's method of compass and straight edge: https://youtu.be/SL2lYcggGpc (probably because folding paper allows you a degree of freedom through the third dimension, instead of remaining stuck in the second). So getting perfect 72 degree angle by folding (depending on your accuracy) has something to do with that.

...

Through my fiddling, I discovered:

1) It's easier to make that first corner-to-point fold (after folding the square in half) by just marking that spot, rather than find it by creasing, because the more creases your paper has, the harder it is to be accurate; it's the corner of a square 1/4 the size of your original (so, on a 12"x12" square, it's at 3"x3").

2) It's also easier to be accurate if you "curl" the paper slightly by running your fingernail across the the crease, so the folded paper starts curling a bit in the direction you want.

3) After the star is cut out, it's easier to get all the creases going in the right direction if you score them, first. If you're into scrapbooking or card making, and have scoring stylus, you can use that. I just used a ball-point pen and drew on the creases, pressing hard, over a foam mat (a mouse pad would work). First, I decided which side I wanted to be the back/inside (as if the finished star were a bowl), and on that side I traced the long creases (the ones from center to point-tip). Then I turned it over and did the same thing for the short creases (from center to "valley").

I think I'll make some more, today. :-)