3.1 Geometry of -spheres I:
Calculate the volumes and surfaces of spheres with in
3,6,12 and 100 dimensions. In evaluating use the
Stirling approximation
.

3.2 Geometry of -spheres II:
For the various -spheres of the foregoing example, compute
the fraction of the total volume contained in a shell between
and . Comment the result.

3.3 Approximate formula for
:
Choose your own example to verify the validity of the approximation
3.30. Put the meaning of this equation in words; demonstrate
the geometrical meaning for a three-dimensional sphere
- even if the approximation is not yet valid in this case.
Make a few runs with Applet Entropy1 and comment on
your findings.

3.4 Sackur-Tetrode equation:
Calculate the entropy of an ideal gas of noble gas atoms; choose
your own density, energy per particle, and particle mass (keeping
in mind that the gas is to be near ideal); use the mimimal
grid size in phase space,
.