Compound transformations

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Sort the frieze patterns into seven pairs according to the way in which the motif is repeated.

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

These grids are filled according to some rules - can you complete them?

This problem is based on the idea of building patterns using transformations.

Experimenting with variables and friezes.

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?