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Friezes by Bob Burn
Friezes by Bob Burn
This booklet on friezes is the second on symmetry in the plane. The first being "Sorting by symmetry, patterns with a centre".
The learning idea is to look at and make figures, notice what they have in common and argue about it.
Now with a new sequel: ‘Wallpaper and Tessellations’
The Bob Burn series
class="linklist"There are three publications in this series of booklets which provide a wealth of information and activities around pattern and symmetry.
- Sorting by symmetry, patterns with a centre: available from the ATM shop
- Friezes: look at and make figures, notice what they have in common and argue about it
- Wallpaper and Tessellations: a further look into symmetries
Sorting by Symmetry: Patterns with a Centre
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.
Friezes
This booklet on friezes is the second of a triplet on symmetry in the plane. The first being "Sorting by symmetry, patterns with a centre".
With ‘Friezes’, as with the earlier book, you will need squared paper, tracing paper and hand mirrors for the suggested activities. Access to a dynamic geometry package and to a version of LOGO will also be useful.
The learning idea is to look at and make figures, notice what they have in common and argue about it.
The material was developed with intending primary school teachers who had a strength in mathematics.
In Patterns with a Centre, reflections and rotations with a common fixed point were explored, and were combined to form cyclic and dihedral patterns. Although the main result in Patterns with a Centre is not used in this booklet, some basic ideas about symmetry which were developed in Patterns with a Centre are used here.
Wallpaper and Tessellations
Wallpaper is made in rolls. One roll of wallpaper shows a frieze pattern. But when two sheets of wallpaper are be laid side by side in such a way that the join matches the pattern and is imperceptible, many sheets may be joined to make the pattern cover an unlimited area.
Wallpaper patterns always allow translations in two (or more) directions. This means that there is neither a point nor a line which is fixed by all the symmetries of a wallpaper pattern.
