Origami Constructions of Rings of Integers of Imaginary Quadratic Fields

TL;DR

This paper demonstrates how origami folding techniques can be used to construct rings of integers of imaginary quadratic fields, linking geometric origami methods with algebraic number theory.

Contribution

It introduces a method to realize rings of integers of imaginary quadratic fields via origami constructions, extending previous algebraic results.

Findings

Origami constructions can generate rings of integers of imaginary quadratic fields.

The paper extends prior algebraic results to geometric origami methods.

It establishes a new connection between origami geometry and algebraic number theory.

Abstract

In the making of origami, one starts with a piece of paper, and through a series of folds along seed points one constructs complicated three-dimensional shapes. Mathematically, one can think of the complex numbers as representing the piece of paper, and the seed points and folds as a way to generate a subset of the complex numbers. Under certain constraints, this construction can give rise to a ring, which we call an origami ring. We will talk about the basic construction of an origami ring and further extensions and implications of these ideas in algebra and number theory, extending results of Buhler, et.al. In particular, in this paper we show that it is possible to obtain the ring of integers of an imaginary quadratic field through an origami construction.