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?

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

These are the interactivities for the article 'Volume of a Pyramid and a Cone on NRICH website. They might take a very long time to load on some computers.

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

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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.

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.

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

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.