File:Shapley–Folkman lemma.svg
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 666 × 333 pixels. Other resolutions: 320 × 160 pixels | 640 × 320 pixels | 1,024 × 512 pixels | 1,280 × 640 pixels | 2,560 × 1,280 pixels.
Original file (SVG file, nominally 666 × 333 pixels, file size: 5 KB)
File information
Structured data
Captions
Summary[edit]
DescriptionShapley–Folkman lemma.svg |
English: The Shapley–Folkman lemma. The sixteen dark red points on the right are the Minkowski sum of the four nonconvex sets on the left, each of which consists of a pair of red points. The plus sign marks a point belonging to the (shaded) convex hull of the Minkowski sum; according to the lemma, this point may be represented as a sum of four points, one for each term in the Minkowski sum. Because the ambient space is two-dimensional, two of these four points belong to the convex hulls of their summands, and the remaining two belong to the summands themselves. |
Source | Own work |
Author | David Eppstein |
Licensing[edit]
Public domainPublic domainfalsefalse |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 20:54, 19 October 2010 | 666 × 333 (5 KB) | David Eppstein (talk | contribs) | {{Information |Description={{en|1=The Shapley–Folkman lemma. The sixteen dark red points on the right are the Minkowski sum of the four nonconvex sets on the left, each of which consists of a pair of |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
File usage on other wikis
The following other wikis use this file:
- Usage on ar.wikipedia.org
- Usage on el.wikipedia.org
- Usage on en.wikipedia.org
- Minkowski addition
- Zonohedron
- Portal:Mathematics/Suggestions
- User:Kiefer.Wolfowitz
- Oriented matroid
- Wikipedia talk:WikiProject Images and Media/Illustration taskforce
- Shapley–Folkman lemma
- Talk:Shapley–Folkman lemma/GA1
- User talk:David Eppstein/2010d
- User talk:Kiefer.Wolfowitz/Archive 5
- Ivar Ekeland
- User:Kiefer.Wolfowitz/Sandbox/SFS
- Wikipedia talk:WikiProject Mathematics/Archive/2012
- Wikipedia:Featured picture candidates/November-2012
- Wikipedia:Featured picture candidates/Shapley–Folkman lemma
- Wikipedia talk:WikiProject Mathematics/Archive/2012/Nov
- User talk:Kiefer.Wolfowitz/Archive 46
- Talk:Shapley–Folkman lemma/Archive 4
- Usage on es.wikipedia.org
- Usage on hy.wikipedia.org
- Usage on it.wikipedia.org
- Usage on ko.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on ro.wikipedia.org
- Usage on ru.wikipedia.org
- Usage on sr.wikipedia.org
- Usage on zh.wikipedia.org