Timeline for Range for radius of tangent sphere to three given spheres
Current License: CC BY-SA 4.0
26 events
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| Jun 11 at 14:28 | history | edited | Quadrics | CC BY-SA 4.0 |
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| S Jun 11 at 0:15 | history | bounty ended | Quadrics | ||
| S Jun 11 at 0:15 | history | notice removed | Quadrics | ||
| Jun 11 at 0:15 | vote | accept | Quadrics | ||
| Jun 10 at 16:11 | vote | accept | Quadrics | ||
| Jun 10 at 16:25 | |||||
| Jun 10 at 15:41 | answer | added | Intelligenti pauca | timeline score: 2 | |
| Jun 10 at 13:19 | answer | added | mathlove | timeline score: 3 | |
| Jun 10 at 9:18 | history | edited | Quadrics | CC BY-SA 4.0 |
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| Jun 10 at 5:58 | comment | added | Quadrics | Yes. Exactly..... | |
| Jun 10 at 3:08 | comment | added | Alex Ravsky | Then I think that we have to consider three critical cases when the $xy$ projection of the center $C_4$ of the fourth sphere belongs to a side of the triangle formed by the projections of the $C_1$ $C_2$, and $C_3$ onto the $xy$ plane and then choose the smallest critical radius as the upper bound. | |
| S Jun 9 at 23:36 | history | bounty started | Quadrics | ||
| S Jun 9 at 23:36 | history | notice added | Quadrics | Draw attention | |
| Jun 9 at 15:25 | history | edited | Quadrics | CC BY-SA 4.0 |
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| Jun 8 at 23:56 | history | edited | Quadrics | CC BY-SA 4.0 |
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| Jun 8 at 14:33 | comment | added | Quadrics | @Intelligentipauca If you increase the radius of the fourth sphere above the minimum (determined by Descartes kissing circles theorem), and place this sphere on top of the first three spheres, then at some point, the ($xy$ projection of the) center of this fourth sphere will lie outside the triangle formed by the projection of the $C_1, C_2, C_3$ onto the $xy$ plane. So there is a upper bound to the radius of the fourth sphere. | |
| Jun 8 at 11:13 | history | edited | Quadrics | CC BY-SA 4.0 |
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| Jun 8 at 9:47 | history | edited | Quadrics | CC BY-SA 4.0 |
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| Jun 8 at 9:15 | comment | added | Intelligenti pauca | The fourth sphere doesn't fall down if its radius il greater than $d$, computed from your formula. I don't understand which upper bound you are looking for. | |
| Jun 8 at 7:29 | answer | added | sirous | timeline score: 1 | |
| Jun 8 at 0:28 | comment | added | Quadrics | Yes. This is really helpful, thank you very much. | |
| Jun 8 at 0:27 | history | edited | Quadrics | CC BY-SA 4.0 |
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| Jun 7 at 23:35 | comment | added | Narasimham | en.wikipedia.org/wiki/Kissing_number helpful? | |
| Jun 7 at 22:58 | history | edited | Quadrics | CC BY-SA 4.0 |
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| Jun 7 at 22:34 | comment | added | Quadrics | I am not sure..... | |
| Jun 7 at 22:26 | comment | added | aschepler | The boundary between falling off or not will be when the plane containing $C_1, C_2, C_4$ is vertical, right? | |
| Jun 7 at 22:15 | history | asked | Quadrics | CC BY-SA 4.0 |