Rotations

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?

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

What groups of transformations map a regular pentagon to itself?

Find the shape and symmetries of the two pieces of this cut cube.