Rotations

This problem explores the shapes and symmetries in some national flags.

Create a pattern on the small grid. How could you extend your pattern on the larger grid?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

What groups of transformations map a regular pentagon to itself?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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

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

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 same and what is different about these tiling patterns and how do they contribute to the floor as a whole?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?