Timeline for Center of convex figure
Current License: CC BY-SA 4.0
27 events
| when toggle format | what | by | license | comment | |
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| Oct 27, 2022 at 18:27 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
added 212 characters in body
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| Oct 23, 2022 at 12:33 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
+Przesławski and Yost
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| Oct 23, 2022 at 12:22 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
added 225 characters in body
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| S Oct 21, 2022 at 20:29 | history | bounty ended | Anton Petrunin | ||
| S Oct 21, 2022 at 20:29 | history | notice removed | Anton Petrunin | ||
| Oct 20, 2022 at 13:25 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
+Huas
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| Oct 20, 2022 at 13:02 | vote | accept | Anton Petrunin | ||
| S Oct 20, 2022 at 13:02 | history | bounty started | Anton Petrunin | ||
| S Oct 20, 2022 at 13:02 | history | notice added | Anton Petrunin | Reward existing answer | |
| Oct 20, 2022 at 11:54 | comment | added | Anton Petrunin | @fedja, this is 1-dimensional case, but I see it now --- it is true since it is true for any projection. | |
| Oct 20, 2022 at 11:27 | vote | accept | Anton Petrunin | ||
| Oct 20, 2022 at 11:28 | |||||
| S Oct 20, 2022 at 11:21 | vote | accept | Anton Petrunin | ||
| Oct 20, 2022 at 11:27 | |||||
| Oct 20, 2022 at 11:14 | vote | accept | Anton Petrunin | ||
| S Oct 20, 2022 at 11:21 | |||||
| Oct 20, 2022 at 1:33 | answer | added | fedja | timeline score: 2 | |
| Oct 20, 2022 at 0:01 | comment | added | fedja | @AntonPetrunin If $[a,b]$ and $[c,d]$ are $t$-close, then $a-c, b-d\le t$, so $\frac{a+b}2-\frac{c+d}2\le t$ and we can exchange the intervals to get the other bound. | |
| Oct 19, 2022 at 23:31 | answer | added | Saúl RM | timeline score: 5 | |
| Oct 19, 2022 at 23:14 | comment | added | Anton Petrunin | @SaúlRM still, suppose two line segment are $\varepsilon$-close --- why their midpoints are $\varepsilon$-close? | |
| Oct 19, 2022 at 22:53 | comment | added | Saúl RM | No, I hadn't thought of the barycenter of curvature. The pity is that it doesn't seem easy to check if any of these barycenters work. About the line segments, I think of their boundary as traversing the segment and then traversing it in the opposite direction, so under that definition the middle point is still the barycenter of the boundary | |
| Oct 19, 2022 at 22:49 | comment | added | Anton Petrunin | @SaúlRM BTW it seems that for line segments only, one can choose their midpoints, but I cannot verify it. | |
| Oct 19, 2022 at 22:46 | comment | added | Anton Petrunin | @SaúlRM did you thaut about baryceter of curvature? (In other words baryceter of vertices of polygon with weights proportional to their external angles.) | |
| Oct 19, 2022 at 22:44 | comment | added | Saúl RM | One candidate for which I didn't find an obvious counterexample: the barycenter of the boundary of the convex set (we can parametrize the boundary by unit length and then find the barycenter of that). In segments it is just the middle point | |
| Oct 19, 2022 at 20:13 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
Two triangles with vertices (0,0), (1,1), (-1,1) and (0,1), (1,0), (-1,0).
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| S Oct 19, 2022 at 19:55 | history | suggested | Christophe Leuridan | CC BY-SA 4.0 |
correct spelling
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| Oct 19, 2022 at 19:38 | answer | added | Christophe Leuridan | timeline score: 0 | |
| Oct 19, 2022 at 17:54 | comment | added | Christophe Leuridan | I guess that take the gravity center works, but I am unable to check it. The gravity center of a non-empty compact convex set is $p_F = \lambda_F(F)^{-1} \int_F xd\lambda_F(x)$ where $\lambda_F$ is the Lebesgue measure on the affine space generated by $F$. | |
| Oct 19, 2022 at 17:49 | review | Suggested edits | |||
| S Oct 19, 2022 at 19:55 | |||||
| Oct 18, 2022 at 12:51 | history | asked | Anton Petrunin | CC BY-SA 4.0 |