Doughnuts and the Fourth Dimension

Abstract

Those of you with a sweet tooth are no doubt already familiar with the delicious doughnut, but did you know there is much more to that simple pastry than meets the eye? Here’s an experiment: take a sheet of A4 paper and roll it up, now try to join the two open ends without bending or making any corners on the paper, go on I’ll wait…..impossible right? Well that’s because we are stuck with only three dimensions, add in one more dimension though and you can! What’s more is that if we lived on the surface of that doughnut, the world would look a lot like the surface of the Earth does to us now-flat as far as the eye can see (but a lot sweeter if you choose to eat the soil). My research is on understanding all these ‘flat’ doughnuts (called tori in mathematics) and how to make ...