Timeline for The center of a minimal convex superbody
Current License: CC BY-SA 3.0
24 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Jan 12, 2016 at 0:37 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
complete the removal of the unnecessary assumptions
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| Jan 11, 2016 at 18:48 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
typos
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| Jan 11, 2016 at 18:30 | comment | added | Włodzimierz Holsztyński | @DouglasZare, thank you for this and all your comments. Your suggestion is interesting (and to me--weird, which is good -). I'll stop to think about it. On the other hand my own completion of the conjecture seems to me boringly natural (however, this time it may be harder?). | |
| Jan 11, 2016 at 18:24 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
More precise conjecture
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| Jan 11, 2016 at 18:21 | comment | added | Douglas Zare | There is a slight variation that I think is better: Suppose no larger isometric copy of $B$ fits in $C$. Must some isometric copy of $B$ inside $C$ contain the center of $C$? This would rule out the counterexample by katz, and the disk in a rectangle, but I think there are other counterexamples starting in $\mathbb{R}^3$. This is true if you replace isometry with translation. | |
| Jan 11, 2016 at 17:27 | vote | accept | Włodzimierz Holsztyński | ||
| Jan 11, 2016 at 15:08 | answer | added | Mikhail Katz | timeline score: 4 | |
| Jan 11, 2016 at 7:39 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
another omission filled in.
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| Jan 11, 2016 at 1:42 | comment | added | Włodzimierz Holsztyński | @ToddTrimble, thank you for your justified (at least relatively) criticism. On the other hand Joseph (above) was a bit overdoing it, I'd think. :) | |
| Jan 11, 2016 at 1:36 | comment | added | Włodzimierz Holsztyński | @R.vanDobbendeBruyn, I apologize for missing the conclusion in my version which you have just seen--I lost this during the editing session. Now I hope that everything is finally fine. | |
| Jan 11, 2016 at 1:32 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
,
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| Jan 11, 2016 at 1:21 | comment | added | Todd Trimble | Yes, "bodies" is plural, and I had understood how you are defining that term. Please take my previous comment as a helpful suggestion; Joseph's confusion was understandable. | |
| Jan 11, 2016 at 0:44 | comment | added | R. van Dobben de Bruyn | It is unclear to me where the assumptions end and the statement (that you want to prove) begins. A full stop (.) and/or a connecting word (e.g. 'then') would be useful. | |
| Jan 11, 2016 at 0:16 | comment | added | Włodzimierz Holsztyński | @ToddTrimble, "bodies" is plural (and $\mathbb R^n$ is not a convex body). At least it was not impossible. | |
| Jan 11, 2016 at 0:11 | comment | added | Todd Trimble | It is much more conventional and understandable to write $B, C \subseteq \mathbb{R}^n$. | |
| Jan 11, 2016 at 0:10 | comment | added | Douglas Zare | For any $B$ not containing the center of $C$, we can expand it to almost half of $C$, on one side of a hyperplane through the center. The question is whether any such almost-half of a centrally symmetric figure can be repositioned inside $C$ to cover the center. This should not be the case if you take a skew slice through the center of a cube, but I haven't yet proved that no rotation works. | |
| Jan 11, 2016 at 0:01 | comment | added | Włodzimierz Holsztyński | @JosephO'Rourke, *** $\ B\ C\ \subseteq \mathbb R^n\ \Leftarrow:\Rightarrow\ \left(\left(B\ \subseteq \mathbb R^n\right) \wedge\left(C\ \subseteq \mathbb R^n\right)\right)\ $ *** | |
| Jan 10, 2016 at 23:55 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
Basic correction.
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| Jan 10, 2016 at 23:51 | comment | added | Joseph O'Rourke | What does " $\ B\ C\subseteq\mathbb R^n\ $" mean? That both $B$ and $C$ are subsets of $\mathbb{R}^n$, or that some product of $B$ and $C$ is? | |
| Jan 10, 2016 at 23:50 | comment | added | Włodzimierz Holsztyński | @DouglasZare, thank you. There is a lot of noise between my brain and my typing fingers. What's worse, there is (sometimes :-) a lot of noise in my poor brain as well. I'll edit my Q. | |
| Jan 10, 2016 at 23:46 | comment | added | Douglas Zare | From the title I would guess that you have an inclusion reversed, and you want to allow translations of $tB$. | |
| Jan 10, 2016 at 21:49 | comment | added | Włodzimierz Holsztyński | body $\,=\,$ compact + n-dimensional | |
| Jan 10, 2016 at 21:21 | history | asked | Włodzimierz Holsztyński | CC BY-SA 3.0 |