Size of this PNG preview of this SVG file: 512 × 512 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 768 × 768 pixels | 1,024 × 1,024 pixels | 2,048 × 2,048 pixels.
Original file (SVG file, nominally 512 × 512 pixels, file size: 10 KB)
 | This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
| Description | Visual proof of Lee Sallows's triangle theorem by CMG Lee. 1. Lines from midpoints of edges of length a, b and c (circles) to the opposite vertex split the triangle into 6 regions. 2. Each region is rotated 90 degrees outwards about its hinge, yielding 3 congruent triangles with sides equal and perpendicular to the line segments between the original triangle's vertices and its centroid (2x, 2y and 2z). 3. The process can be repeated on each smaller triangle. 4. Each resulting triangle has sides a/3, b/3 and c/3, similar to but 1/9 the area of the original. |
| Source | Own work |
| Author | Cmglee |
Licensing
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. |
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 | 21:47, 4 March 2024 | | 512 × 512 (10 KB) | Cmglee | {{Information |Description=Visual proof of Lee Sallows's triangle theorem by CMG Lee. 1. Lines from midpoints of edges of length ''a'', ''b'' and ''c'' (circles) to the opposite vertex split the triangle into 6 regions. 2. Each region is rotated 90 degrees outwards about its hinge, yielding 3 congruent triangles with sides equal and perpendicular to the line segments between the original triangle's vertices and its centroid (2''x'', 2''y'' and 2''z''). 3. The process can be repeated on each s... |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
Global file usage
The following other wikis use this file:
- Usage on es.wikipedia.org
