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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 free course, Symmetry, explains such concepts as direct and indirect symmetries, Cayley tables and groups through exercises, audio and video.
After studying this course, 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.
Study this free course
Enrol to access the full course, get recognition for the skills you learn, track your progress and on completion gain a statement of participation to demonstrate your learning to others. Make your learning visible!
In this course 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 course is presented through a series of PDF documents.
This OpenLearn course is an adapted extract from the Open Unviersity course
Copyright & revisions
Originally published: Monday, 18th April 2011
Last updated on: Monday, 22nd February 2016
- Creative-Commons: The Open University is proud to release this free course under a Creative Commons licence. However, any third-party materials featured within it are used with permission and are not ours to give away. These materials are not subject to the Creative Commons licence. See terms and conditions. Full details can be found in the Acknowledgements and our FAQs section.
- This site has Copy Reuse Tracking enabled - see our FAQs for more information.
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All our alternative formats are free for you to download, for more information about the different formats we offer please see our FAQs. The most frequently used are Word (for accessibility), PDF (for print) and ePub and Kindle to download to eReaders*.
- Word (708 KB)
- PDF (1.7 MB)
- ePub 3.0 (47.7 MB)
- ePub 2.0 (580 KB)
- Kindle (202 KB)
- RSS (58 KB)
- HTML (47.7 MB)
- SCORM (47.7 MB)
- OUXML Package (7 KB)
- OUXML File (20 KB)
- IMS Common cartridge
*Please note you will need an ePub and Mobi reader for these formats.