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
trying to describe it in words?
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NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.