Wikimedia Commons

File:Sum of squares for wiki.gif

Original file ‎(1,080 × 608 pixels, file size: 40.15 MB, MIME type: image/gif, looped, 678 frames, 27 s)

Note: Due to technical limitations, thumbnails of high resolution GIF images such as this one will not be animated. The limit on Wikimedia Commons is width × height × number of frames ≤ 100 million.

Captions

Captions

Add a one-line explanation of what this file represents

Summary

edit
Description
English: Proof without words of the formula for a finite sum of squares. The area of the final rectangle which is assembled can be written as 3(1^2 + 2^2 + 3^2 + ... + n^2) and it can also be expressed as the length times height, which is (1+2+3+...+n)(2n+1). Solving for the sum of squares (i.e. 1^2 + 2^2 + 3^2 + ... + n^2) and applying Gauss's Equality yields the result. (Animation inspired from Roger B. Nelsen's book Proofs without Words: Exercises in Visual Thinking.)
Date
Source Own work
Author Aiyopasta

Licensing

edit
I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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/TimeThumbnailDimensionsUserComment
current19:23, 11 September 2020Thumbnail for version as of 19:23, 11 September 20201,080 × 608 (40.15 MB)Aiyopasta (talk | contribs)Cross-wiki upload from en.wikipedia.org

You cannot overwrite this file.

There are no pages that use this file.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Sum_of_squares_for_wiki.gif&oldid=530706254"