Timeline for Conjecture: If circular coins of any sizes are in a convex polygonal frame, with each coin touching exactly one edge, then all the coins can move
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2023 at 22:11 | history | edited | Dan | CC BY-SA 4.0 |
added 5 characters in body
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| Jan 12, 2023 at 13:07 | history | edited | Dan | CC BY-SA 4.0 |
added 286 characters in body
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| Jan 12, 2023 at 5:51 | vote | accept | Dan | ||
| Jan 12, 2023 at 5:51 | history | edited | Dan | CC BY-SA 4.0 |
Shfited new conjecture to a new question.
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| Jan 11, 2023 at 22:15 | comment | added | Dan | @AndrejBauer About the four circles in the trapezoid, here is a demos graph where you can adjust the sliders to move the coins individually. | |
| Jan 11, 2023 at 20:47 | history | became hot network question | |||
| Jan 11, 2023 at 20:00 | answer | added | Iosif Pinelis | timeline score: 23 | |
| Jan 11, 2023 at 15:59 | comment | added | Mark Grant | There is a growing literature on configuration spaces of hard disks. In particular, the paper arxiv.org/abs/1108.5719 by Carlsson, Gorham, Kahle and Mason has some pictures of 5 coins/disks in a square which seem to support your conjecture. Matt Kahle's answer to my MO question mathoverflow.net/q/59563/8103 contains further references. I wouldn't be surprised if Matt or one of his coauthors knows the answer to your question. | |
| Jan 11, 2023 at 15:24 | history | edited | Dan | CC BY-SA 4.0 |
Editted conjecture in response to counter-example
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| Jan 11, 2023 at 15:13 | comment | added | Akiva Weinberger | @AndrejBauer In the state space, the path-connected component of the configuration is larger than a single point. (I'm fairly certain the path-connected components are the same as the connected components, as well.) | |
| Jan 11, 2023 at 15:07 | comment | added | Joel David Hamkins | We need someone skilled to create animations! | |
| Jan 11, 2023 at 15:03 | comment | added | Andrej Bauer | How would we formally define “coins can move”? I feel like my intuition can easily betray me. At the moment it's telling me the four circle in the trapezoid can't move. | |
| Jan 11, 2023 at 14:15 | answer | added | Zach Teitler | timeline score: 31 | |
| Jan 11, 2023 at 14:10 | history | edited | Joel David Hamkins |
edited tags
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| Jan 11, 2023 at 13:52 | history | edited | Dan | CC BY-SA 4.0 |
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| Jan 11, 2023 at 13:22 | history | edited | Dan | CC BY-SA 4.0 |
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| Jan 11, 2023 at 12:42 | history | asked | Dan | CC BY-SA 4.0 |