Notes on Some Geometric and Algebraic Problems Solved by Origami

TL;DR

This paper reviews how origami techniques can solve classical geometric and algebraic problems, including cubic equations, angle trisection, and doubling the cube, by presenting known solutions and theorems.

Contribution

It compiles and explains known origami-based solutions to complex geometric and algebraic problems, highlighting origami's capabilities beyond traditional constructions.

Findings

Origami can solve the general cubic equation.

Origami methods enable angle trisection and doubling the cube.

The paper details proofs of Haga's theorems using origami.

Abstract

Details for known solutions of some geometric and algebraic problems with the help of origami are presented: two theorems of Haga, the general cubic equation, especially the heptagon equation, doubling the cube as well as the trisection of angles $\alpha$, $\pi - \alpha$ and $\pi + \alpha$.