Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
Stage: 4 Challenge Level:
The corners of the stand have to be considered and this means that

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
Stage: 4 Challenge Level:
The corners of the stand have to be considered and this means that
each individual section is not a cylinder. However a little careful
manipulation will reveal that the problem is far from
For the generalisation it might help to reduce the number of
variables you work with to two at a time...
What is the relationship between the length and the volume if the
radius is fixed?
Is there a way you can represent the relationship without just
try