When you’re eating a triangular slice of delicious floppy pizza, do you sometimes find the tip of the pizza droops - so it’s harder to point it to your mouth? Most pizza, if it’s been cooked right, has the same floppiness as a piece of paper (with the added weight of toppings) - so if you hold one end, the other end will naturally curve downward.

But you might have discovered that there’s a trick you can do to make the end of the pizza stay up: if you bend the crust of the pizza upward at the sides, the floppy end of the pizza is more likely to stick out straight.

You might have done this a hundred times before (or, if not, here’s a new trick you can use - you’re welcome!) but it turns out the reason this works is because of a piece of geometry discovered in 1827. A mathematician called Carl Gauss studied the way that shapes curve in three dimensions, called Gaussian curvature.

An important consequence of this (for pizza fans) is that if something is flat but flexible like a piece of paper, you can only bend it one way at a time. A piece of paper might be floppy, but if you roll it into a tube in one direction, it becomes much more rigid in the other direction - it’s more difficult to bend, without crushing or ripping the paper.

This is the same principle behind corrugated cardboard: the ridges in the corrugated layer make it much harder to bend the card in that direction, while it can still bend the other way. It’s also used in roofing materials and has other applications in construction and engineering.

And pizza follows these same rules: it can only curve one way at a time. If you bend the sides of the crust upwards, it’ll have less flexibility in the direction that’s at right-angles to the crust. If the pizza dough is too soggy, it might stretch and droop anyway - but for well-baked Italian-style thin bases, Gauss and his geometry can help you keep it under control.

The same mathematics - understanding how different shapes curve - explain why it’s so difficult to make a map of the globe. The way a sphere curves, in two directions at the same time, is fundamentally different to a flat piece of paper - so in order to make a true map of the globe, you either need to stretch parts of the Earth’s surface (resulting in Greenland looking huge on some maps, when it’s actually 1/14th the size of Africa), or make a map with gaps in, as though you’ve peeled the Earth like an orange.

Many different ways of representing the curved surface of the Earth on a flat page have been proposed - some preserve the area of the countries, which are more useful for political maps, and others keep straight lines straight, which helps with navigation. Which one is most useful depends on what you’re using it for.

So next time you’re sharing a pizza with friends, you can show them this trick and explain it’s thanks to Carl Gauss that we understand the mathematics behind how shapes curve - and why you can’t peel an orange and get a rectangle!

If you want to explore more and discover a different side to maths, visit cityofmaths.co.uk. Hosted exclusively in Leeds throughout 2026 and 2027, the City of Maths is a two-year celebration of patterns, puzzles and play with trails, competitions, events, and lots more to get involved in.