Four-dimensional paper constructions after Möbius, Klein and Boy / Eiji Ogasa.

Format:

Book

Author/Creator:

Ogasa, Eiji, author.

Series:

K & E series on knots and everything ; 0219-9769 v. 78.

Series on knots and everything, 0219-9769 ; vol. 78

Language:

English

Subjects (All):

Four-manifolds (Topology).

Knot theory.

Physical Description:

xxii, 160 pages : illustrations ; 24 cm.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, [2025]

Summary:

"Explore four-dimensional paper constructions inspired by the work of great mathematicians like Möbius, Klein, Boy, Hopf, and others. These creations will help you visualize four-dimensional space and beyond, transporting you to higher-dimensional spaces. This book is designed to solidify your foundations in various areas of mathematics and physics, with a particular focus on topology. If you are familiar with higher-dimensional spaces from loving sci-fi stories, you may find the four-dimensional illustrations in this book especially intuitive. Imagine starting on Earth and traveling straight up into the universe - where would you end up? Perhaps you would travel in one direction only to eventually return to your starting point. Can you imagine what happens during the course of this trip? By engaging with these four-dimensional paper constructions, you will gain a deeper understanding of this fascinating journey"-- Provided by publisher.

Contents:

Introduction : if you start on earth and travel

Straight up into the universe, where will you end up?

Prologue : time machine and teleportation

A sci-fi detective novel

A locked-room mystery

Challenge to the Reader

Solution

R4

Getting out in four-dimensional space

Let's construct Möbius band

Create a Möbius band with paper and scissors

Miscellaneous : Knot theory

Squares and tori

Two circles and a disc

You can do it in four-dimensional space

How to draw four dimensional space

Put and move objects in four dimensional space

The Hopf link and four-dimensional space

A construction using paper, wire, and fire

Miscellaneous : The Time Machine

It is not a torus

The Klein Bottle and R4

How to construct Klein bottle

Constructing the torus 112

Miscellaneous : The Theory of Relativity

One or two sides

Non-orientability

Caution!

Boundary

Klein bottle=2x(Möbius band)

Miscellaneous : Quantum mechanics

It is not the torus or Klein bottle

The 2-dimensional real projective space RP2 and 4-dimensional space

Mobius band and a disc

Make your Boy surface

Prove

Five dimensional space

Miscellaneous : High-dimensional space applied in daily life

2-dimensional manifolds

The 3-dimensional sphere S3

Miscellaneous : black holes, white holes, and worm holes

S1 x S2

3-dimensional manifolds

High dimensional manifolds

Miscellaneous : string theory.

Notes:

Includes bibliographical references and index.

ISBN:

9789819801794

9819801796

OCLC:

1455632991