Virtual Origami: Mathematical Modeling and Computational Realization

Explore the fascinating world of virtual origami in this 26-minute Wolfram video. Delve into the mathematical formalism behind traditional origami using Mathematica's advanced symbolic, numeric, and graphics computation capabilities. Learn about essential fold rules in traditional origami, focusing on squash and outside-reverse folds. Discover how 2D origami geometry compares to Euclidean geometry in terms of constructible points. Examine the extension of Huzita–Justin's rules through the introduction of cuts along creases, simplifying complex folds like the squash fold. Follow along as the video demonstrates the construction of a flying crane, showcasing the effectiveness and expandability of origami virtualization modeling. Gain insights into the history, geometry, and rules of origami, as well as its visualization and verification using Mathematica.

Intro
Outline
What is Origami
History of Origami
Geometry of Origami
Rules
Mathematica
Visualization
Verifier
Traditional Origami
Reverse Fold
Squash Fold