Explain how to construct a regular pentagon accurately using a straight edge and compass.

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

Whirl a conker around in a horizontal circle on a piece of string. What is the smallest angular speed with which it can whirl?

Can you explain what is happening and account for the values being displayed?

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.