Symmetry

problem

A Problem of Time

Age

14 to 16

Challenge level

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?
problem

Encircling

Age

14 to 16

Challenge level

An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?
problem

Rotations Are Not Single Round Here

Age

14 to 16

Challenge level

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only one centre of rotation ? Or if you thought that was impossible, could you say why ?
problem

Rose

Age

16 to 18

Challenge level

What groups of transformations map a regular pentagon to itself?
problem

Dicey Decisions

Age

16 to 18

Challenge level

Can you devise a fair scoring system when dice land edge-up or corner-up?
problem

More Dicey Decisions

Age

16 to 18

Challenge level

The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?
problem

Cut Cube

Age

16 to 18

Challenge level

Find the shape and symmetries of the two pieces of this cut cube.
article
Tournament Scheduling

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.
article
Friezes

Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?
article
Dancing With Maths

An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?