Origami has become a subject of research in mathematics, science and engineering. A growing artistic and scientific field is that of origami corrugations and tessellations as pioneered by Shuzo Fujimoto, David Huffman, Yoshihide Momotani, Ron Resch and others.
Folding paper is also an accessible activity for education.
This page is available online at https://www.foldworks.net/arts-in-steam-2022/
This simulation of paperfolding in Geogebra uses simple elements for a hypnotic animation. Geometric transformations like reflection, rotation and translation show their power.
This corrugation of paper has been pioneered by Shuzo Fujimoto and others: it uses 60 degree geometry but can be generalised to other angles. When made with paper or thin card the motion shown is difficult to achieve, which may lead one to ask why.
See Using Geogebra for Origami for some ideas and techniques for using Geogebra to design, draw and animate origami.
Crease Pattern (CP)
Mountain folds are red and Valley folds are blue.
Other origami corrugations and tessellations
North American Smocking https://www.adriennesack.com/origami/smocking
Deployable structures and mechanisms https://duckduckgo.com/?t=ffab&q=origami+deployable+structures&iax=images&ia=images
Origami and mathematics education
LEARNING MATHEMATICS WITH ORIGAMI by Tung Ken Lam and Sue Pope, Association of Teachers of Mathematics, ISBN 9781898611950
Star Origami: The Starrygami™ Galaxy of Modular Origami Stars, Rings and Wreaths by Tung Ken Lam, , ISBN 9781032022338
Action Modular Origami to Intrigue and Delight, Tarquin Group, ISBN 9781911093947