How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?
Discover a handy way to describe reorderings and solve our anagram in the process.