Timeline for Maximum volume convex body coverable by a unit square
Current License: CC BY-SA 3.0
18 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| S Apr 6, 2017 at 12:34 | history | suggested | Martin Sleziak |
removed deprecated (geometry) tag - see the tag info: http://mathoverflow.net/tags/geometry/info
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| Apr 6, 2017 at 12:33 | review | Suggested edits | |||
| S Apr 6, 2017 at 12:34 | |||||
| Apr 6, 2017 at 10:48 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image links broken; now fixed.
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| May 6, 2012 at 23:55 | comment | added | Joseph O'Rourke | @Yoav: Yes, good question! I never considered that a possibility, but now I see it is not clear. | |
| May 6, 2012 at 21:31 | comment | added | Yoav Kallus | I meant rather whether for a fixed $k$, $V_\max(k)$ is achievable by a definite set of $k$ pieces, as opposed to a limit. | |
| May 6, 2012 at 16:54 | comment | added | Joseph O'Rourke | @Gerhard: Thanks for the typo correction. Your brick achieves 66% of $V_\max$. | |
| May 6, 2012 at 16:41 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| May 6, 2012 at 16:14 | comment | added | Gerhard Paseman | Oops. Should and .094. Gerhard "Master Of Misteaks And Metamisinformation" Paseman, 2012.05.05.9999872... | |
| May 6, 2012 at 16:10 | comment | added | Gerhard Paseman | Small typo: Vmax shold approach 1/6sqrt(pi); that is about 0.94. Gerhard "Ask Me About System Design" Paseman, 2012.05.05 | |
| May 6, 2012 at 13:21 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| May 6, 2012 at 11:36 | comment | added | Joseph O'Rourke | @Yoav: You are right, there could be a difference between one piece without cuts, and one piece with cuts. And I think it likely that $V_\max$ is unachievable for a finite $k$. | |
| May 6, 2012 at 11:33 | comment | added | Joseph O'Rourke | @Gerhard: I clarified that I meant to cover the entire surface. Your $k=2$ idea is quite plausible! | |
| May 6, 2012 at 11:33 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| May 6, 2012 at 6:08 | comment | added | Gerhard Paseman | For k=2 there is the 1 by 2 by 2 brick with volume 1/16. It is hard to see how to do better. Gerhard "Correct Up To Scaling Factor" Paseman, 2012.05.05 | |
| May 6, 2012 at 3:43 | comment | added | Gerhard Paseman | I thinl V_max(k) is unbounded as k goes to infiinity. I assume I am not supposed to cover the entire convex body, but just arrange a connected shape and then take the connvex hull. In that case, cut k many strips to form unit length edges of your favorite polyhedron. Gerhard "Also, I Could Have Misunderstood" Paseman, 2012.05.05 | |
| May 6, 2012 at 2:20 | comment | added | Yoav Kallus | Why is the $k=1$ case "no cuts" and not "one connected piece"? For the cases where cuts are allowed, is it clear that the supremum is realizable? On the side of the convex shape, Blaschke selection says the limit exists, but on the side of the cut up square, the limit could in theory involve thinner and thinner connected spiral strips. | |
| May 6, 2012 at 1:24 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |