Friday Sprog Blogging: snowflakes

The younger Free-Ride offspring cut this snowflake. But look again -- that's not just a snowflake, that's a snowflake with the face of a monkey! Is this what floats down from the sky to make a winter wonderland of the Planet of the Apes? (Would a sufficient number of monkeyflakes be useful in making frozen banana daiquiris?). "No," says younger offspring. "It's just a cool shape for a paper snowflake. Eee-eee-eee-eee!"


We are expecting rain this weekend, not snow. Nonetheless, it is December, so elder offspring and younger offspring decided to make some snowflakes.

i-f78519842c917a0fa1861d25dbedc503-Flake2.jpgWe didn't do any research on good ways to cut snowflakes, or on the symmetry properties of actual snowflakes in the wild (although you can read about real snowflakes at The World's Fair). Upon inspection, the Free-Ride snowflakes are rather less dendritic and rather more plate-like. (The sprogs have been disappointed from some of their previous cutting choices which destroyed the all-in-one-piece-itude of the snowflakes they were trying to construct, and I think this has made them more cautious about the amount of paper they cut away.) As well, our homemade ones aren't very hexagonal. A lot of this had to do with sensible ways to fold the paper from which the flakes were cut. We started with rectangular sheets of used-on-one-side white paper (old thesis chapter drafts, if you must know), and while it's not hard to turn a rectangular sheet into a decent square before you start folding, it's trickier to turn it into a hexagon or even an equilateral triangle. And, if you're starting with a square, the most natural ways to fold it up before cutting seem to be into squarish quarters or into triangular quarters (i.e., folding on the diagonals). You get pretty flakes, sure, but the symmetry can be ... kind of boring.


So, we also tried some less standard folding patterns, and starting with rectangles instead of squares. You can see some of the results here. As younger offspring pointed out, there's a limit to how many times you can fold the paper and still be able to cut bits out to make a snowflake, and I suspect this limit is even more severe with "student" scissors. (When I was a kid, I was told it was impossible to fold a piece of paper in half more than 8 times, but it now appears that the limit is more like 12 times. But your scissors probably won't even go through all the layers created by 8 folds, so you have to make the 4 folds or so that you can manage really count.)

Can any of you mathematicians or origami masters suggest some non-standard folding patterns that produce awesomely beautiful snowflakes? (And, can you describe them adequately in the comments without the benefit of diagrams?)

More like this

way back when i was in school i learned how to make hexagonal snowflakes. fold into the squarish quarters first. then fold that into thirds. of course, thinner paper works better, but i used to do this with regular old notebook paper.

I'm not sure how nonstandard it is, because it's what I was taught when I was in the third grade or so, but the best way I know to manage hexagonal symmetry is:

  • Fold your sheet of paper in half along the long edge, so that the result is 5 1/2 x 8 1/2
  • Mark the center point of the folded edge.
  • Put the paper on a table with the folded edge toward you.
  • Grab one of the corners where the folded edge ends, and fold it along a line that goes through the center of the folded edge at an angle of 60 degrees or so.
  • Fold the other corner over the same way. If you got the angle right on the previous step, the fold line for this step will be exactly where the edge ended up on the previous step. As with the trifold for a business letter, this takes some practice or some trial-and-error, but it's easy to tell when it's right.
  • Fold in half along a vertical line.
  • Cut off the "ears" so that you have an isosceles triangle with a base angle of 30 degrees. Ideally, you want it so the only "raw" edges are on the short edge of the triangle. (You can also cut so that you have a 30-60-90 triangle with the right angle adjacent to the vertical fold, giving you a bit bigger hexagon from the same size paper.)
  • Now you can cut to your heart's content along the short edge, and as long as some part of the folds remains intact along the long edges it should unfold without falling apart.

A quick animation of the way I was taught to fold paper for snowflakes, though upside-down from the way I just described, can be seen here: .

Even though the flash thingy there lets you make as many snowflakes as you like without killing any trees, there's still nothing like wielding your own scissors against a defenseless triangle of paper.

your snowflakes suck, mine rock, can you make a superman symbol on your snowflakes like i can.

By Kevin Burt (not verified) on 18 Dec 2006 #permalink