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.
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
Make a footprint pattern using only reflections.
An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
Can you construct a cubic equation with a certain distance between its turning points?
An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.
In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
Try ringing hand bells for yourself with interactive versions of Diagram 2 (Plain Hunt Minimus) and Diagram 3 described in the article 'Ding Dong Bell'.
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.