Rotations

Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?

Make a footprint pattern using only reflections.

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

This problem provides training in visualisation and representation of 3D shapes. You will need to imagine rotating cubes, squashing cubes and even superimposing cubes!

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

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

Points off a rolling wheel make traces. What makes those traces have symmetry?

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

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

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?