Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T19:37:37.077Z Has data issue: false hasContentIssue false

10 - Folding Manifolds

from Part III - Algebra, Topology, and Analysis in Origami

Published online by Cambridge University Press:  06 October 2020

Thomas C. Hull
Affiliation:
Western New England University
Get access

Summary

Chapter 10 introduces a more abstract approach to studying origami by considering how we might fold a Riemannian manifold in arbitrary dimension.This generalizes origami in several ways:First, instead of folding flat paper we may consider folding two-dimensional sheets that possess curvature, like the surface of a sphere or a torus.Second, instead of folding flat paper along straight line creases that, when folded flat, reflect one side of the paper onto the other, we may consider folding a three-dimensional manifold along crease planes which reflect one side of space onto the other, or fold n-dimensional space along crease hyperplanes of dimension (n?1).Work in this area by Robertson (1977) and Lawrence and Spingarn (1989) is presented along with more decent additions, such as generalizations of Maekawa’s Theorem and the sufficient direction of Kawasaki's Theorem in higher dimensions.

Type
Chapter
Information
Origametry
Mathematical Methods in Paper Folding
, pp. 191 - 216
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×