Hey, to be honest, this is my first time asking for help on such forums, my task sounds like this: What is the methodology for finding how many small spheres (radius r) can fit in a large sphere (radius R), I have been thinking about this for a long time, but I just can’t come to a satisfactory result, all I have now is that if R = 3r, then a maximum of 12 balls can fit in such a sphere (looking ahead - no, the option is to divide the volume of a large sphere by the volume of a small one and round up by the smaller side does not correct). I will be glad to receive any suggestions and even links to literature that can provide some sort of clue. Thank you.
The packing problem: What is the methodology for finding how many small spheres (radius r) can fit in a large sphere (radius R)?
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Dr.Peterson
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Sphere packing in a sphere - Wikipedia
The very nature of this page will tell you that there is probably no straightforward "methodology"; it's an inherently difficult problem.
Beyond that, you might try the bibliography here:
Sphere Packing -- from Wolfram MathWorld
Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for identical spheres: cubic lattice, face-centered cubic lattice, and hexagonal lattice. It was hypothesized by Kepler in 1611 that...
mathworld.wolfram.com