Rotations

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only one centre of rotation ? Or if you thought that was impossible, could you say why ?

Weekly Problem 31 - 2008
The flag is given a half turn anticlockwise about the point O and is then reflected in the dotted line. What is the final position of the flag?

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?

Put your visualisation skills to the test by seeing which of these molecules can be rotated onto each other.

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?

Does changing the order of transformations always/sometimes/never produce the same transformation?

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.