Geometric solution of a quintic equation by two-fold origami

TL;DR

This paper demonstrates a geometric method using two-fold origami to solve any quintic equation, translating algebraic solutions into physical folding procedures with explicit formulas and examples.

Contribution

It introduces a novel origami-based geometric approach to solve quintic equations using only two simultaneous folds, expanding the scope of origami mathematics.

Findings

Two-fold origami can solve arbitrary quintic equations.

Explicit formulas for the folding procedures are provided.

An illustrative example demonstrates the method's application.

Abstract

This article shows how to find the solution of an arbitrary quintic equation by performing two simultaneous folds on a sheet of paper. The folds achieve specific incidences between a set of points and lines that are determined by the coefficients of the quintic. Complete equations for computing the set are given, and their application is illustrated with an example.