Timeline for Thinnest rigid packings of the plane
Current License: CC BY-SA 4.0
12 events
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| Mar 15, 2020 at 13:54 | comment | added | Nandakumar R | The construction given on mathoverflow.net/questions/145314/… probably works for zero density arrangements with half-disks (semidisks) too - this appears to follow from all boundaries between a region with disks and the empty region being concave polylines as noted there. | |
| Mar 14, 2020 at 17:37 | comment | added | Nandakumar R | And Wojowu, I too would like an answer to the question you raised. Thanks | |
| Mar 14, 2020 at 17:31 | comment | added | Nandakumar R | Thanks TonyK. the link you gave shows the construction given in mathworld.wolfram.com/RigidCirclePacking.html is not quite optimal (zero density) - The construction drawn by Prof. O'Rourke does not look a straight enhancement of the picture given in the above Mathworld page. And yes, after some experimentation, I am unable to see how the kind of construction beginning with a hexagonal lattice of disks can be naturally done with unit squares. | |
| Mar 13, 2020 at 20:50 | comment | added | Yoav Kallus | For unit squares I believe you should be able to use the structure in the mathworld illustration, replacing the circles with alternating coordinate-aligned squares and 45-degree-rotated squares so that each square of one orientation is wedged between three squares of the other orientation. | |
| Mar 13, 2020 at 20:06 | comment | added | Wojowu | The question now is: is there a shape which does not admit density zero rigid packings? | |
| Mar 13, 2020 at 19:50 | comment | added | Nandakumar R | thanks... made a corrective edit. | |
| Mar 13, 2020 at 19:49 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Mar 13, 2020 at 18:54 | comment | added | Yoav Kallus | Why do you write "probably" the thinnest? The packing by Böröczky cited on that page and in the linked question has density zero. Are you suggesting there may be ones with negative density? | |
| Mar 13, 2020 at 18:52 | comment | added | TonyK | See this question and answers for packings with zero density. | |
| Mar 13, 2020 at 18:22 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Mar 13, 2020 at 18:21 | history | edited | YCor | CC BY-SA 4.0 |
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| Mar 13, 2020 at 18:20 | history | asked | Nandakumar R | CC BY-SA 4.0 |