top of page

Origami and Mathematics

Is it a bird? Is it a plane? No – it’s Origami!

According to Wikipedia, "Origami is the art of paper folding, which is often associated with Japanese culture. In modern usage, the word "origami" is used as an inclusive term for all folding practices, regardless of their culture of origin."

To those who don’t know much about origami, it might just look like intricate, beautiful, complicated art, but the truth behind it is that it is all about mathematics.

How can paper art be connected to mathematics you might wonder? Well, at the heart of it, Maths is about making sense of the rules and patterns of the universe. We look for patterns everywhere. Have you ever looked at the patterns of a leaf or a snowflake? Origami looks at the geometry of the 'crease pattern' in the paper.

There are valley creases and mountain creases. A mountain crease is a fold where the two ends of paper go down and the fold is pointed upwards. It looks like a mountain. A valley crease is the opposite. The fold is at the bottom, and the ends of paper are facing upwards, to look like a valley. A vertex (corner), is where the mountain and valley creases meet. When working with a piece of paper to make origami, we look where the lines intersect, what angles they form, and if they are mountain or valley creases.

If you are ever lucky enough to hold an intricate piece of origami artwork, you might be tempted to unfold it and see how it was made. If you did, you would see the pattern of creases that act as a blueprint for the piece. The crease pattern is the key to understanding the secret behind how the paper is able to fold into a beautiful model. The door the key unlocks is to a world of fascinating mathematics! explains the science behind pattern theory. When we look at mountain and valley creases, we can turn them into simple equations. If we subtract mountain folds from valley folds (or vice versa), the absolute difference is two. (We don’t include negative numbers.) For example: 5 mountain creases and 3 valley creases would be correct, since 5-3=2. BUT, 6 mountain creases and 2 valley creases wouldn’t work because 6-2=4. This rule is crucial when learning how to read and fold crease patterns, as it can save the artist a lot of time trying to fold 6 mountain creases and 5 valley creases since that’s not possible.

This is just one rule in the secret art of paper folding. There are others and they are all based on mathematics. More laws of origami are that no matter how many times you try to stack folds and sheets, a sheet can never penetrate a fold and that every other angle around the vertices comes out to 180 degrees.

While origami is beautiful to look at, art is not the only contribution it makes to our so