Suppose you have a circular cake or pizza that needs to be cut into six pieces and you don’t have a cooking protractor. How could you cut it into – at least roughly – sixths?

This is something that I’ve always done by eye, and always messed up. Until very recently, when I realised I could harness the power of geometry.

Have a think about it. Solutions below the line.

### Sixths

• Cut a radius ((Finding the centre of the cake is left as an exercise))
• Find the midpoint of the radius
• Eyeball where the perpendicular to that radius meets the cake’s circumference
• Cut a radius to that point
• What you have there is a bona fide sixth of a cake.

The point on the circumference is the same distance from the centre and the end of the first radius, and the two radii are equal, so the angle must be $\piby 3$.