Higher-dimensional origami constructions

Lang, Origami and Geometric Constructions Origami and Geometric Constructions 1 Lang, Origami and Geometric Constructions Introduction

By Robert J. Lang Copyright ©1996–2015. All rights reserved. Introduction ................................................................................................................................... 3 Preliminaries and Definitions ...................................................................................................... 3 Binary Divisions ........................................

Lang, Origami and Geometric Constructions Origami and Geometric Constructions Introduction

Constructions for Higher Dimensional Perfect Multifactors

Perfect maps, factors and multifactors can be viewed as higher dimensional analogues of de Bruijn cycles and factored versions of these cycles. We present a unified framework for two basic techniques, concatenation and integration (also called the inverse of Lempel’s homomorphism), used to construct perfect multifactors. This framework simplifies proofs of known results and allows for extension...

Higher Dimensional Geometries from Matrix Brane Constructions

Matrix descriptions of even dimensional fuzzy spherical branes S in Matrix Theory and other contexts in Type II superstring theory reveal, in the large N limit, higher dimensional geometries SO(2k+1)/U(k), which have an interesting spectrum of SO(2k+1) harmonics and can be up to 20 dimensional, while the spheres are restricted to be of dimension less than 10. In the case k = 2, the matrix descr...

A Mathematical Theory of Origami Constructions and Numbers

About twelve years ago, I learned that paper folding or elementary origami could be used to demonstrate all the Euclidean constructions; the booklet, [9], gives postulates and detailed the methods for high school teachers. Since then, I have noticed a number of papers on origami and variations, [3], [2] and even websites [7]. What are a good set of axioms and what should be constructible all ca...