Sorting by symmetry: patterns with a centre

Bob Burn has gathered a collection of diagrams and geometric objects. Sorting is a natural human activity and here the collection is sorted by symmetry. Choose some favourite symmetrical objects to sort alongside the figures in the first few sections and recognise the groupings for yourself.

Careful observation of symmetrical objects enables us to understand symmetry better, and to explore ways to combine one symmetry with another. In this way we find how rotations and reflections combine with themselves and with each other, which leads to the discovery that all the symmetry groups we have been looking at are either cyclic, and consist only of rotations, or have an equal number of rotations and reflections. The booklet gives a clear structure for most symmetry work in school, except for friezes and tessellations. The activities are appropriate, at various levels, for Key Stage 2 and upwards. Some familiarity with length and angle is presumed, but no previous experience is needed with symmetry or groups.