World Library  
Flag as Inappropriate
Email this Article

Dissection (geometry)

Article Id: WHEBN0008780235
Reproduction Date:

Title: Dissection (geometry)  
Author: World Heritage Encyclopedia
Language: English
Subject: Kepler–Poinsot polyhedron, Diabolical cube, Hill tetrahedron
Collection:
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Dissection (geometry)

In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another). It is usually required that the dissection use only a finite number of pieces.

The Bolyai-Gerwien theorem states that any polygon may be dissected into any other polygon of the same area. It is not true, however, that any polyhedron has a dissection into any other polyhedron of the same volume. This process is possible, however, for any two honeycombs (such as cube) in three dimension and any two zonohedra of equal volume (in any dimension).

A dissection into triangles of equal area is called an equidissection. Most polygons cannot be equidissected, and those that can often have restrictions on the possible numbers of triangles. For example, Monsky's theorem states that there is no odd equidissection of a square.[1]

See also

References

External links

  • Dissection Tiling.
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.