Talk:Primary pseudoperfect number

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Field:  Number theory

Image

The image presently in the article doesn't explain why it demonstrates that "1 = 1/2 + 1/3 + 1/11 + 1/23 + 1/31 + 1/(2×3×11×23×31)." If no explanation is forthcoming, it should be deleted from the article. — Arthur Rubin (talk) 16:51, 12 March 2013 (UTC)

Because it's a square (with side length that can be taken as one) divided into smaller squares (with side lengths 1/2, 1/3, etc), with each band of smaller squares having area 1/2, 1/3, etc because the number of squares in the band are 2, 3, etc. So area 1 = area 1/2 + area 1/3 + ... etc. By expanding out the one-dimensional sum into two-dimensional squares, the fact that the side lengths of each square are the correct value becomes visually evident, because no other size of square could exactly fill out the unit width by that number of copies. And before you ask for reliable sources explaining all of this: that would be a ridiculous demand that would prevent us from illustrating anything, because if such sources existed then using images sourced by them would very likely be a copyright violation. —David Eppstein (talk) 19:12, 12 March 2013 (UTC)
The overall edge lengths needs to be labeled as "1" and 1-1/(2×3×11×23×31). Then it would be an adequate explanation, IMO. The that, and any further detail, would fall under WP:CALC. Without that, it's not much better than the "proof" that 5×13=8×8. — Arthur Rubin (talk) 20:09, 12 March 2013 (UTC)
It is not intended to be a drawing of a rectangle. It is intended to be a drawing of a unit square. However, because the final row of tiny squares would be so tiny, it has been omitted from the drawing as an optimization in order to save illustration effort and file size without creating any change to the actual visual appearance of the drawing. —David Eppstein (talk) 01:04, 13 March 2013 (UTC)
That looks like the discussion on "it goes without saying" in Mathematics Made Difficult. It would fail the "proof without words" section of Mathematics Magazine. I still don't think it's illustrative. — Arthur Rubin (talk) 02:07, 16 March 2013 (UTC)
It is confusing not to show the last area "1/(2×3×11×23×31)", but doing so is not practical. A simple solution of this dilemma is to replace the image with one showing instead that 42 is primary pseudoperfect. Jsondow (talk) 15:57, 6 April 2017 (UTC)