Timeline for How to pack a sphere with cubes?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2019 at 21:58 | comment | added | CommaToast | Still not seeing an acceptable answer. Is there really no formula or Python script in existence to calculate this...? | |
| Mar 15, 2017 at 10:21 | answer | added | Adam Bailey | timeline score: 5 | |
| Mar 14, 2017 at 23:46 | comment | added | richard1941 | consider a description of the solution. each cube would have a position (defined by x,y,z coordinates) and an orientation vector defined by unit vector u,v,w). So get out your excel spreadsheet and start jiggling things. You need a way to check if a cube intersects the surface of the sphere, and a way to check if a cube intersects another cube. for me, it got ugly fast, but you can probably guess that simulated annealing is one of my favorite procedures. And watch out for local extremes! | |
| Mar 14, 2017 at 6:05 | comment | added | Gerry Myerson | There is some discussion at au.mathworks.com/matlabcentral/newsreader/view_thread/278586 | |
| Mar 14, 2017 at 3:11 | comment | added | BobaFret | You can also establish a lower bound by considering the volume of the largest cube that can be inscribed in a sphere of radius 5: $(10/ \sqrt{3})^3$ | |
| Mar 14, 2017 at 2:39 | comment | added | Qudit | @Rahul I'm sure that's true if the size of the cubes is not too much smaller than the radius of the sphere. However, I suspect that the optimal packing is as I've said above if the radius is large. | |
| Mar 14, 2017 at 2:36 | comment | added | user856 | @Qudit, Seth: The optimal packing can be a bit more complicated than that in 2D, and I see no reason why the 3D case should be simpler. See also packing cubes in cubes. | |
| Mar 14, 2017 at 2:34 | comment | added | Seth Wyma | This is true. How could I got about finding the extra volume? | |
| Mar 14, 2017 at 2:33 | comment | added | Qudit | Cubes pack together cleanly (unlike spheres) so the empty space will all be around surface of the sphere. | |
| Mar 14, 2017 at 2:23 | history | asked | Seth Wyma | CC BY-SA 3.0 |