Does changing the order of transformations always/sometimes/never produce the same transformation?
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?
My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?
A red square and a blue square overlap. Is the area of the overlap always the same?
Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
