Talks - Alastair Stanley: Computational Origami

Origami geometry (origammetry) can be used for mathematical calculations and solving equations, including cubic and quartic equations

The fundamental operations of origami are defined by 7 core axioms that describe different types of folds (point-to-point, line-to-line, etc.)

A Python library called “origammetry” was created to simulate origami folds and solve mathematical problems computationally

Using origami, it’s possible to:

• Construct rational numbers and fractions
• Prove that √2 is irrational
• Find roots of cubic equations
• Create geometric constructions like perpendicular lines

The Belloc fold (Axiom 6) is particularly powerful, allowing simultaneous alignment of points onto lines to solve complex equations

Multi-fold origami (making multiple folds simultaneously) is theoretically possible but practically challenging

Brittany Gallivan proved in 2002 that paper could be folded 12 times in the same direction, disproving the “can’t fold more than 8 times” myth

Origami constructions can produce geometric ratios like the golden ratio (φ) without requiring measuring tools

While origami can solve many mathematical problems, it has limitations - it cannot directly construct π or solve infinite-order polynomials

The practical applications are limited by physical constraints like paper thickness and alignment precision, making computer simulations more practical for complex calculations