So, why does a big slice of pizza tend to droop unless you fold it into a curve? Well, there’s some math involved in all this pizza folding: the basic concept here deals with the 19th century principle of Gaussian curvature.
Wired’s Aatish Bhatia used the pizza question as a nice starting point to explain this unique aspect of geometry, and once you understand this principle, you’ll never look at pizza the same way again.
Well, it’ll still look delicious of course, but you get my point.
Check out what Aatish had to say after the break…
Well, the pizza slice was flat before you picked it up (in math speak, it has zero Gaussian curvature). Gauss’s remarkable theorem assures us that one direction of the slice must always remain flat — no matter how you bend it, the pizza must retain a trace of its original flatness. When the slice flops over, the flat direction (shown in red below) is pointed sideways, which isn’t helpful for eating it. But by folding the pizza slice sideways, you’re forcing it to become flat in the other direction – the one that points towards your mouth. Theorema egregium, indeed.
By curving a sheet in one direction, you force it to become stiff in the other direction. Once you recognize this idea, you start seeing it everywhere. Look closely at a blade of grass. It’s often folded along its central vein, which adds stiffness and prevents it from flopping over. Engineers frequently use curvature to add strength to structures. In the Zarzuela race track in Madrid, the Spanish structural engineer Eduardo Torroja designed an innovative concrete roof that stretches out from the stadium, covering a large area while remaining just a few inches thick. It’s the pizza trick in disguise.