Solving for Xmas: how to make mathematical Christmas cards

With less than a month to go before Christmas Day, it's time to start thinking about cards. Here Oxford maths don Vicky Neale explains how to impress your friends with these stunning geometrical designs. It's Christ-maths time, and there's no need to be afraid.

Christmas is a fantastic opportunity for me to share some maths with friends and family. One of my favourite ways to do this is by stitching geometrical designs on cards. The magic is how the straight lines produce perfect curves.

Here's how it's done. Draw two straight lines that intersect. Draw points along each of those lines at equal distances. When you join the dots from one line to the other, as in the star and tree above and in the four images below, you get a parabola. Strictly speaking, the curve is the envelope of the family of straight lines.