Timeline for Characterizing Convex Configurations of Quadrupels of Coplanar Points via Linear (In-)equalities between Distance Sums or Differences
Current License: CC BY-SA 3.0
10 events
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| Jun 13, 2017 at 11:12 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
deleted 21 characters in body
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| Feb 17, 2013 at 23:37 | history | edited | Günter Rote | CC BY-SA 3.0 |
added 79 characters in body
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| Feb 17, 2013 at 19:52 | comment | added | Günter Rote | @Lee, I don't get what you mean. By comparing sums or differences I understand something like $AB < AC-BD$. The OP does not talk about comparing the length $BD$ to the length $BD$ of another instance. | |
| Feb 17, 2013 at 19:30 | comment | added | Włodzimierz Holsztyński | Lee, author's guidance is a possibility. Another is that once the question is out in public, and it's not exact, then the readers create the most tasty, juicy, fruitful, ... interpretations, open to doing mathematics. This latter was the case--of leaving room for interpretations--even with some of the famous Hilbert problems, hey! :-) So, it's a bit like in poetry. --* The author dies at the delivery of their poem. | |
| Feb 17, 2013 at 14:25 | comment | added | Lee Mosher | I interpreted the OP's wording differently: since the value of the diagonal BD itself has changed, then you can distinguish these three examples by the sum/difference expression "BD", in which the sum and the difference sign each appear zero times. Perhaps the OP can give us some guidance on what intepretation was intended. | |
| Feb 17, 2013 at 12:55 | history | edited | Günter Rote | CC BY-SA 3.0 |
correction to adapt to the figure
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| Feb 17, 2013 at 5:19 | comment | added | Włodzimierz Holsztyński | This is a very minimal (hence elegant) argument. But if additions and sums allow repetitions (i.e. we need to consider linear combinations with arbitrary integer coefficients--which is here equivalent to rational coefficients) then I wonder if additional work is needed; at least I don't see a full proof immediately. | |
| Feb 17, 2013 at 1:39 | comment | added | Joseph O'Rourke | @Günter: I think you had your labels scrambled? I tried to fix them. Apologies if I altered your intention! Feel free to undo my changes. | |
| Feb 17, 2013 at 1:37 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Added image, tried to fix labels...
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| Feb 17, 2013 at 1:14 | history | answered | Günter Rote | CC BY-SA 3.0 |