# Paper Folding

Paper folding or Origami, as it is traditionally known, is one of the oldest forms of paper sculpting that is still practiced in its entirety today. The concept of using a simple piece of paper and creating a shape, almost any shape, out of it means that not only is it extremely easy for someone to start pursuing this hobby, there is also very little chance that one might get bored off of it. Paper folding is something that you really need to experience to understand the kind of satisfaction and joy that comes out of creating something beautiful out of something so simple.

What many people, even those who are extremely experienced in this hobby, fail to realise is that there is a massive connection between paper folding and mathematics. In the 18th century, the Germans found out that paper folding really increased the rate of development of a child's mind, and without knowing it, began using a scientific technique that is understood much better today.

**The Basic Connection**

From a very general perspective, it is quite easy to see how paper folding is connected to mathematics or, to be more specific, geometry in particular. Every folded sculpture that you make is not just a piece of art that you have created, it is also a combination of a number of different geometrical figures that have combined to become the final piece that you see. To understand this better, simply start unfolding what you've made and you will see a number of geometrical shapes all over it, in a number of different angles and sizes.

For e.g. a simple waterbomb base will have, when completely unravelled, a set of about 8-right triangles. Even in the case of the bird base, you will find a lot more triangles in number and you will also realise that every time you make a reverse fold to create a neck or a tail, you will actually end up adding another four triangles to that paper. A squash fold, when unwrapped, creates an angle that has been bisected twice and such a fantastic connection between these two fields ensures that Origami, or paper folding, is not just something you do to have fun!

**Advanced Connections**

There is something really special about paper folding when you start making the comparison to something that is more complicated. For e.g. when making the traditional crane, one of the most popular forms of Japanese Origami and also a symbol of good luck, you end up creating a crease-pattern where, at any point or vertex on the flat paper, the sum total of all the angles being formed will always be 180 degrees.

That, in essence, is what the Kawasaki Theorem, in geometry, states. This is the kind of information that a student can use to learn about the theorem or, better still, this is the kind of interesting and entertaining method that a teacher can use to teach students about what the theorem actually means. Not only do the students enjoy making something, they also learn about something important and not by trying to follow an uninteresting method of being taught out of a book or having to read what's written on the blackboard.

**Topology Connections**

Paper folding has also been considered similar to graph theory wherein topology becomes a subject directly linked with this art-form. Now, while most people do know about geometry and have encountered it in some form or the other, throughout school and college, making that connection is simpler. However, not everyone understands or encounters topology and people may go through their entire education without even hearing of the term or understanding what it means.

Topology is nothing but a modern version of geometry where you study space in all its different forms. It basically states that any shape can be made into any other shape, and retrieved as the original shape, as long as there are no holes, cuts or breaks made during the conversion process. As a result, this form of geometry states that a circle is the same as a square or a rectangle or a triangle because by simply pulling at the lines that form a circle, you can make the corners that will help you create these squares or rectangles or triangles.

So, if you can create a square from the same lines that form a circle, then it is the same as you creating a Tyrannosaurus Rex out of a small piece of paper - as a result, paper folding to create shapes is the same as topology. Topology is one of the most basic forms of geometry known today and it is also the study that has helped us understand how the mind perceives objects in the perspective, thereby helping us to make them as we see them.

What this means is that if you consider a plate lying on a table and look at it from directly above the plate, it appears completely round. However, if you look at the plate from an angle, then it will appear like an ellipse, even though the actual shape of the plate hasn't changed. Paper folding, to create shapes, is another great way of demonstrating how the paper, even though it changes shape, is all about the perspective from which you are looking at it rather than an actual change of form. That, in a nutshell, is the application of paper folding in a world where learning and fun go together!