Geometrische Konstruktionen und Origami
Kay Paulus

TL;DR
This paper surveys the algebraic foundations of origami, especially Galois theory, develops fundamental foldings, explores constructible fields, and applies these to classical geometric construction problems.
Contribution
It introduces a systematic framework of fundamental origami foldings and analyzes the algebraic structures they generate, linking origami to Galois theory and classical constructions.
Findings
Developed a system of fundamental foldings.
Identified the field of constructible numbers via origami.
Applied the framework to classical geometric problems.
Abstract
The aim of this article is to give practicing teachers an overview about the theory behind paperfolding, it is my qualifying thesis(Zulassungsarbeit) as a teacher in Germany. It is a survey about the relations between paperfolding and algebra, in particular Galois theory. We develop a system of fundamental foldings for paperfolding, discuss which field can be constructed using these techniques and advance to concrete constructions solving (classical) construction problems. Finally, we think about possible generalisations of the given system of fundamental constructions. Das Ziel dieser Arbeit ist es, aktiven Lehrern einen \"Uberblick \"uber die algebraische Theorie hinter Origami zu geben, der Artikel ist meine Zulassungsarbeit. Es handelt sich um einen \"Ubersichtsartikel \"uber die Relationen zwischen Origami und Algebra, insbesondere Galoistheorie. Wir entwickeln ein System von…
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Taxonomy
TopicsAdvanced Materials and Mechanics · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · Art, Technology, and Culture
