One of the most important patterns that a mathematician looks for is whether or not an object has symmetries i.e. is left unchanged or invariant after some operation, for example reflection or rotation. A square has many symmetries under the operations of rotation and reflection whereas a rectangle has fewer symmetries. The concept of a group of symmetries measures and describes how much symmetry an object has. This concept of a group is one of the most important in mathematics and also helps to describe and explain the natural world.

The transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and-events/symmetries-and-groups
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