File:The sum of the first n odd integers is n². 1+3+5+...+(2n-1)=n²..gif
%3Dn%C2%B2..gif){kind=small}
No higher resolution available.
The_sum_of_the_first_n_odd_integers_is_n²._1+3+5+...+(2n-1)=n²..gif (683 × 598 pixels, file size: 1,018 KB, MIME type: image/gif, looped, 61 frames, 20 s)
 | 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 |
English: The first n odd integers viewed on a tetrahedron give a proof without words that their sum is n². The animation shows a 3D view of a tetrahedron which when rotated gives two representations of the same number : either stacked rows of consecutive odd numbers of dots 1, 3, 5,... or a square array of n² dots. |
| Date | |
| Source | Own work |
| Author | V.pantaloni |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:30, 29 December 2019 | | 683 × 598 (1,018 KB) | V.pantaloni | Optimized to less than 1MiB |
| 12:11, 28 December 2019 |  | 683 × 598 (1.39 MB) | V.pantaloni | Cross-wiki upload from en.wikipedia.org |
File usage
The following page uses this file:
Global file usage
The following other wikis use this file:
- Usage on ar.wikipedia.org
- Usage on el.wikipedia.org
- Usage on eml.wikipedia.org
- Usage on fr.wikipedia.org
- Usage on id.wikipedia.org
- Usage on lv.wikipedia.org
- Usage on ru.wikipedia.org
%3Dn²..gif){kind=link}