FoldTheorem: Origami Checker

Explore the geometry of paper folding with FoldTheorem, a specialized tool designed for origami enthusiasts, students, and professional designers. This application provides a robust environment to analyze the flat-foldability of vertex patterns using established mathematical principles.

Whether you are designing a complex original model or studying computational geometry, FoldTheorem helps you verify your designs instantly. By entering mountain and valley creases, you can determine if a vertex can be folded completely flat without paper tension or self-intersection.
Key Features:
• Interactive Vertex Design: Use the visual dial to build and adjust crease patterns with high precision.
• Live Analysis Dashboard: Get instant feedback as you work. The app calculates total angles and foldability status as you add or modify creases.
• Mathematical Validation: Full support for Maekawa’s Theorem and Kawasaki’s Theorem, providing clear pass/fail results for each rule.
• Quick-Add Presets: Speed up your workflow with one-tap buttons for standard origami angles like 22.5°, 45°, 60°, and 90°.
• Pattern History: Save your successful patterns to a personal history for later reference or further study.
• Educational Tool: Learn the logic behind flat-foldability through an intuitive interface that makes abstract geometric concepts tangible.

FoldTheorem bridges the gap between artistic creativity and mathematical rigor. Perfect for anyone looking to deepen their understanding of how complex origami structures behave in 2D space.