File talk:Fano plane with nimber labels.svg
Arrangement[編集]
Hi. Do you prefer the present arrangement of the numbers for some reason?
If not I would like to replace it by the following:
2 010
3 6 011 110
7 111
1 5 4 001 101 100
The binary representation would be symmetrical, and it would correspond to
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where the vertices are numbered by the correspondence with | .svg)
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. |
Greetings, Watchduck (talk) 14:20, 1 November 2011 (UTC)
- Your arrangement is isomorphic to the present one; pictorially it corresponds to a reflection along the line 3–7–4. I see no clear reason to prefer one isomorphic presentation over another one. As the vertices in the Fano plane in the Hasse diagram are not numbered, I don't see the correspondence as an argument. What is the point of that diagram anyway? The middle two layers show that the Fano plane is self-dual, but in that context the top and bottom layers are only visual noise. --Lambiam 20:39, 1 November 2011 (UTC)
When I have to choose a random presentation I always choose symmetry. That's why I mentioned the binary numbers. The enumeration of the vertices in the Hasse diagram is not shown, because that wouldn't be readable - but the other two Hasse diagrams don't leave a choice for their enumeration. They are also the reason, that the top and the bottom vertex are shown. I wouldn't make a Hasse diagram of a lattice of subgroups without the group itself on the top and the trivial group on the bottom. And I make corresponding files as similar as possible.
I don't want to use contradicting files together, so I would upload a Fano plane that corresponds with my other files. But before I wanted to ask, if we can change this one instead. That's all. Greetings, Watchduck (talk) 23:52, 1 November 2011 (UTC)
