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'Turning Granny' printed from http://nrich.maths.org/

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Watch this short video clip:
This text is usually replaced by the Flash movie.

Make a granny knot and a reef knot for yourself.

Now investigate their symmetries. Start with the granny knot.
Does it look the same after a half turn about a vertical axis?
How about after a half turn about a horizontal axis from right to left?
Now try a half turn about a horizontal axis front to back. Does it look the same this time?
(Don't forget you can play the video again to remind you of these three axes.)

Try the same thing with a reef knot.

What is the same about the symmetries of the two knots?

What is different?