A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
Age 11 to 14 Challenge Level:
Here are two sets of graphs. Each shows a pair of lines which are
reflections of each other, one in the horizontal axis and one in
the vertical axis.
Move the green and yellow dots on the interactivity below to create
some more pairs of reflected lines. Full screen version
What can you say about the equations of two lines if one is a
reflection of the other in the horizontal axis? What about a
reflection in the vertical axis?
Below are the equations of sixteen
straight lines. Each line has a partner, either its reflection in
the horizontal axis or its reflection in the vertical axis. Without
plotting any graphs, can you find all the pairs and say which axis
they were reflected in?
Now imagine that a line is reflected
in one of the axes and the image is then reflected in the
Can you predict the equation of the
resulting line if you know the equation of the original?
Does it make a difference which axis you choose to reflect in
Explain your findings.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.