Why does bending a pizza slice help you eat it? Dig in to the math of the 'fold hold'. NationalPizzaDay
If you zoom in on an ant that lives on the cylinder, there are many possible paths the ant could take. It could decide to walk down the curved path, tracing out a circle, or it could walk along the flat path, tracing out a straight line. Or it might do something in between, tracing out a helix.
Gauss’s brilliant insight was to define the curvature of a surface in a way that takes all these choices into account. Here’s how it works. Starting at any point, find the two most extreme paths that an ant can choose . Then multiply the curvature of those paths together . And, voila, the number you get is Gauss’s definition of the curvature at that point.Let’s try some examples.
That's because bending doesn't change any distances on the surface, and so the ant living on the surface would still calculate the same Gaussian curvature as before. This might sound a little abstract, but it has real-life consequences. Cut an orange in half, eat the insides , then place the dome-shaped peel on the ground and stomp on it. The peel will never flatten out into a circle. Instead, it’ll tear itself apart. That’s because a sphere and a flat surface have different Gaussian curvatures, so there’s no way to flatten a sphere without distorting or tearing it.
? Same problem. No matter how you bend a sheet of paper, it'll always retain a trace of its original flatness, so you end up with a crinkled mess.
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