The power of multifolds: Folding the algebraic closure of the rational numbers

TL;DR

This paper explores how multifolds in origami can be used to construct the algebraic closure of rational numbers, extending origami's geometric capabilities beyond classical angle trisection.

Contribution

The paper introduces the concept of n-parameter multifolds and demonstrates their use in constructing the algebraic closure of rational numbers, advancing origami geometry.

Findings

One-parameter multifolds can generate the algebraic closure of rationals.

Multifolds extend origami's ability to solve algebraic problems.

The approach bridges origami constructions with algebraic number theory.

Abstract

It is well known that the usual Huzita-Hatori axioms for origami enable angle trisection but not angle quintisection. Using the concept of a multifold, Lang has achieved quintisection but not arbitrary algebraic numbers. We define the n-parameter multifold and show how to use one-parameter multifolds to obtain the algebraic closure of the rational numbers.