Origami and Math

 This blogpost is inspired by the Ted talk by Robert Lang called The Math and Magic of Origami.

Origami is the ancient art form of folding a single sheet of paper to create objects.  You can make animals, hearts, boxes, the list never ends. In fact, the amount of objects that could be made with origami exploded once people incorporated math.  So why not incorporate origami in the math class?
Not only would students learn about an ancient culture, but it will teach them some properties about geometry and it will be super engaging because students will be able to make their own creation.  Also, origami is great because if you mess up you just unfold it and try again.  And students could probably choose their own figure to make, so it would allow for different levels of skill.  In fact I could see making a project that would include a part about learning about the culture surrounding origami, then making an origami figure and explaining the math behind their figure.  For example, Robert Lang talks about numbering the angles around the center circle and seeing that after folding, the odd numbered angles would add to be a line and the even numbered angles would add to be a line.  I think this is super interesting and it would be interesting to ask students to find angle measures based on how many folds there are.

You could also have the students examine the crease patterns (the flat unfolded page that was once folded) and ask if there are any congruent shapes and why.  Are there any similar shapes?  You could also have them take a ruler to the paper and ask them area of different shapes in the crease pattern as well as perimeter.  I think there are a lot of skills that could be practiced by doing this origami.

Robert Lang also discusses applications of origami in the real world.  Some examples he discusses are heart stints and telescopes.  I think it would be a great idea to have students work in pairs and present on a real application of origami that uses math properties that we had talked about in class.

I think this would be a really fun and engaging way to talk about shapes and geometry while learning a skill that students can be proud of.  It also provides a way to learn about another culture which will help students become better citizens of the world.  With the added component of researching a real life application of origami, we are also extending what we have learned and seeing how these things really matter, which is something a lot of math classes don't address.  Overall, I think it's a very interesting application of math and creates such beautiful objects.

Happy folding!