File:3 utilities problem proof.svg
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 512 × 341 pixels. Other resolutions: 320 × 213 pixels | 640 × 426 pixels | 1,024 × 682 pixels | 1,280 × 853 pixels | 2,560 × 1,705 pixels.
Original file (SVG file, nominally 512 × 341 pixels, file size: 3 KB)
File information
Structured data
Captions
Summary
[edit]Description3 utilities problem proof.svg | Proof without words that the three utilities problem has no solution by CMG Lee. The leftmost house is first deleted. The lines connecting the utilities with the remaining houses divide the plane into three regions, shaded yellow, red and blue. Whichever region the deleted house is placed into, one of the utilities is outside the region. The Jordan curve theorem states that a line connecting them must intersect one of the existing lines. | ||||||
Source | Own work | ||||||
Author | Cmglee | ||||||
Other versions |
|
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:57, 13 March 2021 | 512 × 341 (3 KB) | Cmglee (talk | contribs) | Shade regions with the colour of the utility outside it. | |
19:48, 8 March 2021 | 512 × 341 (3 KB) | Cmglee (talk | contribs) | Centre graphic and shade white region. | ||
13:44, 28 February 2021 | 512 × 341 (3 KB) | Cmglee (talk | contribs) | Use simpler proof | ||
05:48, 28 February 2021 | 512 × 341 (3 KB) | Cmglee (talk | contribs) | {{Information |Description=Proof without words that the three utilities problem has no solution by CMG Lee. The three dashed lines are first deleted. The remaining lines divide the plane into two regions, shaded white and purple. Two of the dashed lines can be restored, one crossing the inside region, the other crossing the outside. As there are no regions left, the remaining line cannot be restored without crossing either line. |Source={{own}} |Date= |Author= Cmglee |Permissi... |
You cannot overwrite this file.
File usage on Commons
The following 7 pages use this file:
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org
- Usage on www.wikidata.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Short title | 3 utilities problem proof |
---|---|
Image title | Proof without words that the three utilities problem has no solution by CMG Lee. The leftmost house is first deleted. The lines connecting the utilities with the remaining houses divide the plane into three regions, shaded yellow, red and blue. Whichever region the deleted house is placed into, one of the utilities is outside the region. The Jordan curve theorem states that a line connecting them must intersect one of the existing lines. |
Width | 100% |
Height | 100% |