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Mario has a whole pizza that hasn’t been cut. He cuts the pizza in half, and then cuts each of those pieces in half to make four pieces. He then cuts all of those slices in half, and then those in half and so on.

Take a sheet of A4 paper and measure its sides. A4 is 210 millimetres wide and 297 millimetres long. It’s probably the most common size of paper and it’s used in most countries. However, A4 side lengths aren’t simple numbers like 200 or 300 millimetres. So why don’t we use something easier to measure?

Do you own a dog? Do you ride a bike to school? Do you have black hair? Each of these questions divides people into two groups – you either have a dog, or you don’t.

A few months ago, scientists from the Large Hadron Collider announced they had found a new particle, one that could be the Higgs boson. The Higgs particle is thought to have properties explaining how other particles have mass. But the first signs of this new particle were detected over a year ago.

Imagine a flat spiral, similar to a snail’s shell, coming closer and closer to a point. Now imagine more spiral lines, all centred on the same point. This shape looks like the clouds over a cyclone, or a whirling galaxy.