Maths and music

Task 3a: the Symmetries of a Square

Draw a square on squared paper, labelling the corners as in this diagram:

Now turn the square through 90 degrees clockwise about its centre. It looks exactly the same, except that the position of the labels has changed:

This is a symmetry of the square. See if you can find them all – you should find 8 altogether, including the symmetry where you leave the square alone. Basically, you are looking for all the operations on the square you can find that end up with the square looking just the same as when you started. An example of an operation on the square which is not a symmetry of the square is a rotation through 45 degrees clockwise about the centre of the square, because the square doesn't look exactly the same after you've done the operation:

When you think you've found all 8 symmetries, check your answers.

Answers to Task 3a
Now return to Chris' talk

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