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# Folding Puzzles

The abstract mathematics of origami.

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Prepare yourself to think logically and creatively to figure out some paper folding challenges!

In this unit, we explore some profound mathematics that relates to origami (paper folding). In particular, we’ll focus on geometric questions that you can ask about how paper can be folded and about the physical results of different folding instructions.

Although each fold is a simple crease, when you fold many times in a row and then cut or punch a hole, the resulting patterns can be very surprising. For example:

If you fold a piece of paper in half 3 times as shown above and then punch a hole all the way through the multiple layers of folded paper, how many holes will there be and where will those holes be when you unfold the paper?

For one final example of the complexities that can result from simple folding patterns, consider the sequence of shapes below. Each is made using very simple rules for folding and unfolding a long wire or strip of paper.

These shapes are known as dragon curves. Watch what happens as the number of folds used to make the design increases: