Follow hints using a little coordinate geometry, plane geometry and
trig to see how matrices are used to work on transformations of the
Can you construct a cubic equation with a certain distance between
its turning points?
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.
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
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.
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.
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
Make a footprint pattern using only reflections.
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
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'.
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.
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.