A tower of squares is built inside a right angled isosceles triangle. What fraction of the area of the triangle is covered by the squares?

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

How much of the square is coloured blue? How will the pattern continue?

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?

Hilbert's Hotel has an infinite number of rooms, and yet, even when it's full, it can still fit more people in!

Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses. . . .

This article gives a proof of the uncountability of the Cantor set.