Estimation quiz!

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(08-02-2020 05:04 PM)Maximilian Hohmann Wrote:  … I only found one paper online with an equation for this problem: Nelson M. Blachman: The Closest Packing of Equal Spheres in a Larger Sphere (1963) …

An interesting read:
 Grundlehren def mathematischen Wissenschaften 290
  Sphere Packings, Lattices and Groups
   ISBN 978-1-4757-2016-7 (eBook)
    © 1988 by Springer Science+Business Media New York

"                        PREFACE
This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, … . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? …
…
1. The Sphere Packing Problem
1.1 Packing ball bearings. The classical sphere packing problem, still unsolved even today, is to find out how densely a large number of identical spheres (ball bearings, (I) for example) can be packed together. To state this another way, consider a large empty region, such as an aircraft hangar, and ask what is the greatest number of ball bearings that can be packed into this region. If instead of ball bearings we try to pack identical wooden cubes, children's building blocks, for example, the answer becomes easy. The cubes fit together with no waste space in between, we can fill essentially one hundred percent of the space (ignoring the small amount of space that may be left over around the walls and at the ceiling), and so the number of cubes we can pack is very nearly to the volume of the hangar divided by the volume of one of the cubes.
   But spheres do not fit together so well as cubes, and there is always some wasted space in between. No matter how cleverly the ball bearings are arranged, about one quarter of the space will not be used."

BEST!
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ps: the book is in at least a third edition