Monday Morning Math: Origami

Good morning!  This is the first Monday in May and the trees and flowers are in bloom.  It’s also finals week at Naz, which means it’s the last Monday Morning Math of the school year.  I hope you’ve had fun – we’ll pick it back up in September, probably starting the Monday after Labor Day!  Same bat time, same bat channel.

For this final MMM we’re using a reader suggestion – Origami (thanks Phyllis!)  Origami is a pretty neat subject [one that I think we’ll come back to next year too] because you can use it to make things like a flapping bird:

or a modular pinwheel:

Want something more geometrical?  Here’s a whole page that shows you how to make all the Platonic Solids (symmetric three dimensional polyhedron made out of a single regular polygon) AND all the Archimedean Solids (same as Platonic, but using more than one shape) AND some stars.

Want something more practical?  How about a giant space telescope made out of origami: 

Too big? What about medical implants?

Or do you just want to see some pictures of origami?

Here’s a fish:

CC by Emre Ayaroğlu

Here’s some more fish, each made from a dollar bill:

CC by Qualiesin

Here’s a lilac spider, in honor of the upcoming Lilac Festival:

CC by Robert Salazar

And, finally, here’s a pretty figure in case you didn’t want to end with a spider:

CC by praaeew

Have a good summer/winter everyone [depending of course on which hemisphere you’re in]!  My own plans include making even more origami – I got this book by Thomas Hull but haven’t had a chance to make things from it yet.  I hope your own plans are equally fun!

Origami in the News

Godzilla likes to fold origami. So do many others. Robert J. Lang, for example, has a great web page with some beautiful origami creations. Lang’s work is art, but his expertise has also been used to solve science problems.

One such problem is how to get a really big telescope into space. Bigger than the Hubble telescope. A lot bigger: the lens of the planned telescope is 100 meters, compared to 2½ meters for the Hubble. The solution that Lang worked on was to fold the lens so that it would be small enough to fit in a rocket, but could unfold in space and work. There’s a picture of a prototype (still bigger than Hubble’s lens) and a much more detailed story of the problem and solution here.

Another problem has to do with airbags: how can airbags be folded so that, as they are released, they are strong enough to prevent injury in an accident but flexible enough to avoid causing injury themselves? To address this, Lang used principles of origami rendered into computer code. A video and the complete story are available here.

I learned of Lang’s work through this article on MAA Online a few days ago.

It’s a bird! It’s a plane! Oh, wait, it IS a plane.

This news story made the rounds many months ago, but I didn’t read of it until I was paring down my Inbox this week (1388 messages. It was getting a little overwhelming) and found it in a news digest. In late March, the Japan Aerospace Exploration Agency accepted a proposal of a project led by Shinji Suzuki to make origami spacecrafts and launch them from the International Space Station. How cool is that?

One worry is that they would burn up because friction from entering the atmosphere tends to make things rather hot, but it’s possible/likely that they won’t both because of their shape and because they will be traveling so slowly through the atmosphere (plus the paper, made from sugar canes, is heat resistant). When I first read this I envisioned Giant Origami Planes, but they’re actually small: the shuttles will only be 8 inches by 4 inches after folding, and weigh just over an ounce.

Another worry is that there is no way of controlling where they land, or even how to track them. This is a much bigger deal, and perhaps one reason they’re not going with the Giant Origami I’d envisioned (can you imagine if one of those swooped down onto your lawn?). But don’t go looking too soon: the grant they received is for 3 years of feasibility studies.

While you’re waiting, you can learn how to make an Origami Rocket.

I read this story in many places, but got most of the info for here from Discovery News.

Hoorah for the Hexadecagon!

There was a Hexadecagon in the New York Times Wednesday, in an article about glassblowing. First the article talked about people blowing glass at the Corning Museum GlassLab:

Except the glassblowers weren’t from 1955. Then the article explored the creation of glass designs, including knit glass (!!!) and New York City inspired pretzels. And, as promised in the title, there was also a hexadecagon. It looked a little like this

Except in wasn’t in Las Vegas. And it had 16 sides.

With that inspiration, I looked up hexadecagon to see what I could learn about it. I found that a hexadecagon is also known as a hexakaidecagon, and can be constructed with a straightedge and compass. And I found that origami madness made a neat origami design with four hexadecagons:

Photo by origami madness. Some rights reserved.

Here it is unfolded:

Photo by origami madness. Some rights reserved.

And oschene made some Fujimoto cubes with hexadecagonal irises (irides?)

Photo by oschene. Some rights reserved.

Photo by oschene. Some rights reserved.

And finally, the Imperial Seal of Japan (Crest of Chrysanthemum) isn’t quite a polygon, but if it were then it would be a hexadecagon.

Licensed under Creative Commons Attribution ShareAlike

Passover Math: Origami frog

Passover starts today (in an few minutes or so). When I think of passover I think of matzah balls, and indeed there is a whole slew of matzo math (about halfway down that page) that was posted just a few days ago. But when I did a search on Passover, I also found a bunch of stuff about frogs, presumably because frogs were Plague #2 of the Ten Plagues. And when I thought of frogs, I thought of origami, which is automatically mathy because of all that geometry.

So here are directions on how to make a jumping origami frog!