File:Erdős–Anning proof.svg
Original file (SVG file, nominally 441 × 360 pixels, file size: 29 KB)
Captions
Summary edit
DescriptionErdős–Anning proof.svg |
English: Illustration for a proof of the Erdős–Anning theorem, that a non-collinear set of points in the plane with integer distances must be finite. Given three non-collinear points A, B, C in the set (here, the vertices of a 3-4-5 right triangle), the points whose distances to A and to B differ by an integer must lie on a system of hyperbolas and degenerate hyperbolas (blue), and symmetrically the points whose distances to B and to C differ by an integer must lie on another system of hyperbolas (red). Any point that has integer distance to all three of A, B, C must lie on one of the finitely many intersections of a blue and a red curve. Each branch of a hyperbola is labeled by the integer difference of distances that is invariant for the points on that branch. |
Date | |
Source | Own work; hyperbolas scaled from File:Simple Hyperbola.svg |
Author | David Eppstein |
Licensing edit
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 06:07, 19 March 2023 | 441 × 360 (29 KB) | David Eppstein (talk | contribs) | Uploaded own work with UploadWizard |
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 en.wikipedia.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.
Width | 441 |
---|---|
Height | 360 |