Image:Znam-2-3-11-23-31.svg

From Wikipedia, the free encyclopedia

Znam-2-3-11-23-31.svg‎ (SVG file, nominally 396 × 396 pixels, file size: 7 KB)

Wikimedia Commons logo This is a file from the Wikimedia Commons. The description on its description page there is shown below.
Commons is a freely licensed media file repository. You can help.
Description

Graphical demonstration that 1 = 1/2 + 1/3 + 1/11 + 1/23 + 1/31 + 1/(2×3×11×23×31). Each row of squares has k squares of side length 1/k, for some k in the set {2,3,11,23,31,47058}; for instance the first row has two squares of side length 1/2. Thus, each row of squares has area 1/k, and all six rows together exactly cover a unit square. The bottom row, with 47058 squares of side length 1/47058, would be too small to see in the figure, and is not shown. Sets of integers such that 1 = \sum 1/x_i + \prod 1/x_i, such as the set {2,3,11,23,31} used to construct this figure, correspond to solutions of Znám's problem. As all numbers in the set {2,3,11,23,31} are prime, their product 47058 is a primary pseudoperfect number.
Source

Originally from en.wikipedia; description page is/was here.
Date

2006-12-05 (original upload date)
Author

Original uploader was David Eppstein at en.wikipedia
Permission
(Reusing this image)

Released into the public domain (by the author).

[edit] License information

Public domain This image has been (or is hereby) released into the public domain by its author, David Eppstein at the wikipedia project. This applies worldwide.

In case this is not legally possible:
David Eppstein grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

[edit] Original upload log

(All user names refer to en.wikipedia)

  • 2006-12-05 01:51 David Eppstein 256×256×0 (5661 bytes) Graphical demonstration that 1 = 1/2 + 1/3 + 1/11 + 1/23 + 1/31 + 1/(2×3×11×23×31). Each row of squares has k squares of side length 1/k, for some k in the set {2,3,11,23,31,47058}; for instance the first row has two squares of sid

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeDimensionsUserComment
current02:27, 25 August 2007396×396 (7 KB)David Eppstein ({{Information |Description=Graphical demonstration that 1 = 1/2 + 1/3 + 1/11 + 1/23 + 1/31 + 1/(2×3×11×23×31). Each row of squares has k squares of side length 1/k, for some k in the set {2,3,11,23,31,47058}; for instance the first row has two squares)
The following pages on the English Wikipedia link to this file (pages on other projects are not listed):