A sphere 5.5 metres in diameter is filled with 1m diameter hemi-spheres.
(a) What is the theoretical maximum amount of hemi-spheres that can be crammed into the big sphere given that the following condition is met:
Each hemi-sphere's flat side (which I'll now refer to as its 'disc') has a central point (indicated by the white point shown in the hemisphere diagram to the right). The point must not 'see' another hemisphere's disc. By definition, when I say 'see', the simplest thing to imagine is a straight ultra-thin 'laser light' coming from the disc. This 'light' must not reach another disc. However, if there's another hemi-sphere that's 'blocking' the 'line of sight', then this is accepted.
(b) By cramming them as efficiently as possible, a relatively small volume will be left. How large is this volume? as efficiently as possible, a relatively small volume will be left. How large is this volume?