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 , 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.
This work has been released into the public domain by its author, David Eppstein at English Wikipedia. This applies worldwide. In some countries this may not be legally possible; if so: David Eppstein grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.Public domainPublic domainfalsefalse
Original upload log
The original description page was here. All following 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
Captions
Add a one-line explanation of what this file represents
copyrighted, dedicated to the public domain by copyright holder<\/a>"}},"text\/plain":{"en":{"P6216":"copyrighted, dedicated to the public domain by copyright holder"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P6216 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed">
released into the public domain by the copyright holder<\/a>"}},"text\/plain":{"en":{"P275":"released into the public domain by the copyright holder"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P275 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed">
{{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
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):