How is Origami Math?


Will be elaborated, and spell-checked/revised soon. I just wrote what my heart told me to, and my heart isn't grammatically correct most of the time :) I am posting this unfinished so my readers can have some content.


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 How can Origami be Math?

 

Introduction 

  Have you ever folded a crane? If not, you can follow the instructions on  This link. Your first crane probably won't be pretty ,if you even manage to fold it. You start by folding the paper in half. You are dividing by two. To make the base, you make eight isosceles right triangles. When you make the wings, you are constructing a right triangle with predetermined legs. Every step of almost every origami piece can be described like this. Because of this, its not surprising that when you unfold the crane the crease patterns on the paper make angles that are 60º, 90º, 45º, 30º, and other angles with mathematical signifigance.  It isn't shocking that a lot of the figures formed by the crease lines are congruent and often regular polygons. Every fold in the crane makes some mathematical figure. But did the original creator of the crane try to do that? No. He didn't lose any sleep over whether he made common angles in the creases. So why are the creases so mathematically "perfect"? Like everything in the universe, origami abides to general rules. You will very seldom come across an origami project which says "Vally fold a random section of the paper to the other side". You instead fold to an existing crease or edge. If you are always folding to an existing crease, you are just making a geometric construction.

   

Okay, it might be math. Who cares, and how is this useful?

    Everyone cares about origami, whether they know it or not. Mathematicians love origami because it shows, in a real life setting, the beauty of mathematics. If you don't love origami because of the insight into mathematics it gives, (precious few people enjoy math for its pure beauty) perhaps you can enjoy it because of the insight into the world it gives you! 

    Our DNA is made from folds, our skin folds, our clothing folds, essential proteins in our body fold. When I say something, the air is folding, pleating, making waves. Life is practically made from origami. Take a piece of paper. Crumple it up into a small ball. There are mountains and valleys and places where absolutely nothing is happening. This is what the crust of earth does; over thousands of years folding over itself, it folded all of the breathtaking geographical oddities we adore.

     Looking at the bigger picture,  our galaxy, and other galaxies are swirling and rotating and folding over themselves. Understanding folds, and consequently origami, helps us understand the world around us. Ever since I started origami, it has helped me visualize rotations and translations much better. When I was in Boy Scouts, building structures and doing physical tasks became immensely easier because I was able to translate it into an origami problem. The restrictions on a piece of paper are very similar to the restrictions on reality.

    Many inventions are based on origami. Getting electronics to fold (and therefore occupy less space) is a large issue in most electronics companies. Satellites are beginning to make their panels fold up into a common origami tessellation to avoid damage, make transportation easier, and reduce fuel consumption. Robert Lang, a physicist,  devoted much of his work to origami. Thanks to this, he has brought to the world  many inventions  and a lot of understanding. I suggest you research him, for my origami is inspired by him greatly. 

    When cars crash, origami saves the lives of everyone involved. Because of the heaviness of cars and the speeds they travel at, cars have an enormous amount of energy. In a head on collision, the energy should instantly kill everyone in the collision, because the energy in the car would be transfered to the participants. While they still claim many lives, plenty of car crashes transfer their energy into  folding the hood of the car into an accordion instead of killing people. After the cars hit, an air bag expands to protect the riders. Some important questions are how do we fold this bag so that is opens safely, quickly, and still occupies little room. All of these questions boil down to origami.

    I highly suggest you research this subject if it interests you. Look in the "Links and Resources" section for some sources you can start with. E-mail me if you find anything interesting, and I might add it to the webpage. If you include a name and request credit for the find, I will definitely cite you at the bottom of the article.

TODO: Add learning and fun sections