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

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

Can you fit polynomials through these points?

An arithmetic progression is shifted and shortened, but its sum remains the same...

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.

Can you work out the natural time scale for the universe?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Is it possible to find the angles in this rather special isosceles triangle?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?