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Regular divisions

Introduction

From time to time certain models require us to begin with a regular grid crease pattern. Of course, this can be easily prepared by using ruler and pencil, however, it is also possible to complete the task without such auxiliary tools.

How can a square be divided into "n" equal sections by folding only? The answer is fairly simple in case of the various powers of two, as cascading divisions into half are sufficient to do the job. For the rest we need more serious geometric tricks. Yet, a few well-chosen folds can lead us to the desired divisions. Below you can find two "recipes" for dividing a square's side into thirds and fifths (the particular solutions presented here are not exclusive). Note that by further halving you can easily divide into sixths, and tenths as well.

For those who would like to dive deeper into this topic, I recommend Robert Lang's handy software called ReferenceFinder, which can generate folding sequences to find or approximate any given point or line on a square-shaped paper. What more, it provides you with fine instructions, too!

The diagrams below are free to download for personal use only.
In all other cases my permission is required.

| division into thirds | division into fifths |

Division into thirds

The diagrams below are free to download for personal use only.
In all other cases my permission is required.

| division into thirds | division into fifths |

Division into fifths


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