Symmetries & Groups - Professor Raymond Flood

13 Dec 2013 01:54 63
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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.

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