from The Open University
Alternatively you can skip the navigation by pressing 'Enter'.
A History of Ideas - How do I live a good life?Monday, 30th March 2015 12:04 - BBC Radio 4Melvyn Bragg and his four guests delve deeper into the philosophy of how we live a good life. Read more: OU on the BBC: A History of Ideas - How do I live a good life?
Timewatch: StonehengeAvailable until Friday, 24th April 2015 11:00Two of Britain’s leading archaeologists and world-renowned experts on Stonehenge, Professor Tim Darvill and Geoff... Read more: OU on the BBC: Timewatch - Stonehenge
Turn your bank holiday into a badged holidayWhat are your plans for the long weekend? DIY? A trip to a windswept beach? Why not take your... Read more: Turn your bank holiday into a badged holiday
Take the photographic memory testCan you capture scenes just by looking at them? Find out with our photographic memory test. Launch now: Take the photographic memory test
Early years team work and leadershipThis unit explores aspects of teamwork and leadership for early years practitioners. Try: Early years team work and leadership now
Succeed with maths – Part 1[BETA] If you feel that maths is a mystery that you want to unravel then this short 8-week course... Try: Succeed with maths – Part 1 now
We all encounter symmetry in our everyday lives, in both natural and man-made...
We all encounter symmetry in our everyday lives, in both natural and man-made structures. The mathematical concepts surrounding symmetry can be a bit more difficult to grasp. This unit explains such concepts as direct and indirect symmetries, Cayley tables and groups through exercises, audio and video.
By the end of this unit you should be able to:
- explain what is meant by a symmetry of a plane figure;
- specify symmetries of a bounded plane figure as rotations or reflections;
- describe some properties of the set of symmetries of a plane figure;
- explain the difference between direct and indirect symmetries;
- use a two-line symbol to represent a symmetry;
- describe geometrically the symmetry of a given figure which corresponds to a given two-line symbol;
- find the composite of two symmetries given as two-line symbols;
- find the inverse of a symmetry given as a two-line symbol;
- write down a Cayley table for the set of symmetries of a plane figure;
- appreciate how certain properties of the set of symmetries of a figure feature in a Cayley table;
- explain the meaning of the terms group, Abelian group and the order of a group;
- give examples of finite groups and infinite groups;
- determine whether a given set and binary operation form a group by checking the group axioms;
- deduce information from a given Cayley table;
- understand that the identity in a group is unique;
- understand that each element in a group has a unique inverse;
- recognise how the uniqueness properties can be proved from the group axioms;
- explain the connections between properties of a group table and the group axioms;
- describe the symmetries of some bounded three-dimensional figures;
- use two-line symbols to denote symmetries of three-dimensional figures, and to form composites and inverses of such symmetries;
- count the number of symmetries of certain polyhedra;
- understand why there are exactly five regular polyhedra.
In this unit we use the geometric concept of symmetry to introduce some of the basic ideas of group theory, including group tables, and the four properties, or axioms, that define a group.
Please note that this unit is presented through a series of PDF documents.
This unit is an adapted extract from the Open Unviersity course