Edited by Jane Rosemarin
The math behind the origami. Drawing by Hadi Tahir.
See PDF diagrams.
There are already a lot of tutorials available on how to make a pentagon from a square. This is another way of doing it. It starts with first finding the (√5-1)/8 of the length of the paper to get a 36° angle. If you find the diagrams confusing, you can watch the video below. Thank you!