Exploring and noticing

A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

How can you decide if a graph is traversable?

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.

In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.

Complex numbers can be represented graphically using an Argand diagram. This problem explains more...

Where do people fly to from London? What is good and bad about these representations?

This problem challenges you to sketch curves with different properties.