Jordan Ellenberg On How Geometry Explains the World

 Jordan Ellenberg On How Geometry Explains the World

So you’re walking down the street carrying a hot slice of pizza on a paper plate. The tip of the slice is so heavy with cheese and sauce that it’s drooping toward the ground. How do you solve this problem?

Naturally, you fold the pizza lengthwise, New York–style. But why does warping the pizza by turning the crust ends toward each other keep the molten cheese at the pizza tip from falling on the street? The answer is geometry.

Pizza has a surface with zero curvature, which means a slice resists bending both vertically and horizontally at the same time (unlike the double curvature of, say, a Pringle chip). Your brain intuits this without any assistance from geometric theory. But the theory exists anyway. In 1827, Carl Friedrich Gauss proved the Theorema Egregium—roughly “Awesome Theorem”—which, extremely simplified, says that you can’t change an object’s curvature and keep its geometry intact. An orange peel has…

Read full article…www.theatlantic.com