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Order of Rotation
By Puzzled Dad on Wednesday, October 11, 2000 - 08:50 pm:

My daughter's homework has two questions on rotation which we do not understand. Apparently the order of rotation of a circle is infinite. Also the order of rotation of the letter H is 2.
Why is this????

By Dan Goodman (Dfmg2) on Thursday, October 12, 2000 - 02:58 pm:

The "order of rotation" is the number of angles you can rotate it through leaving it looking exactly the same.
So, with H you can rotate it through 0 degrees, which is the same as rotating 360 degrees, or you can rotate it through 180 degrees. However, with a circle you can rotate it through any angle you like, and it will still look like the same shape, so it has infinite order of rotation. You might like to try and work out the order of rotation of a square and a pentagon and other regular polygons, see if you notice a pattern.

By The Editor :

Another way of thinking of it is "the number of ways up it looks the same". You can try tracing a shape and turning the tracing round, and seeing how many ways up you can put it on the original.