The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

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?

Use Farey sequences to obtain rational approximations to irrational numbers.