Image:Sylvester-square.svg

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Sylvester-square.svg‎ (SVG file, nominally 410 × 410 pixels, file size: 5 KB)

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Description

Graphical demonstration of the sum of the reciprocals of Sylvester's sequence,

1 = \frac12 + \frac13 + \frac17 + \frac1{43} + \frac1{1807} + \cdots

The first row of 2 squares has side length 1/2, for total area 1/2, the second row of 3 squares has side length 1/3, for total area 1/3, etc. All the squares together fill out the area of a unit square, showing that the total area is 1. Only the first four rows are shown; the bottom row is at distance 1/1806 from the bottom side of the unit square, a distance too small to easily be seen in the figure.
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 01:23 David Eppstein 256×256×0 (3909 bytes) Graphical demonstration of the sum of the reciprocals of [[Sylvester's sequence]], :<math>1 = \frac12 + \frac13 + \frac17 + \frac1{43} + \frac1{1807} + \cdots</math> The first row of 2 squares has side length 1/2, for total area 1/2, the second row of 3 s

File history

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Date/TimeDimensionsUserComment
current02:27, 25 August 2007410×410 (5 KB)David Eppstein ({{Information |Description=Graphical demonstration of the sum of the reciprocals of Sylvester's sequence, :<math>1 = \frac12 + \frac13 + \frac17 + \frac1{43} + \frac1{1807} + \cdots</math> The first row of 2 squares has side l)
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