This is silly. Every math textbook that teaches Theorema Egregium includes the same pizza example. That's how I learnt it as well. In my case we had an animated math professor who chose to bring a slice of pineapple pizza with canadian bacon to class, but during his demonstration the pineapples combined with the bacon and turned all gooey and started dripping on his shirt, so Theorema Egregium had to take a backseat to the practical realities of maintaining spotless formal attire in the classroom in front of a hundred giggling freshmen.
But seriously, this Theorema Egregium => Eating Pizza example is straight out of recreational math[1] & is very popular.
standard numerical geom text [2]:"In our everyday life we encounter the Theorema Egregium in a pizzeria..."
another riemann geom text[3]: "There is an interesting real-life application of Theorema Egregium...Notice that when you hold the pizza in one hand, the principal curvature of the crust is much smaller than along the direction of falling toppings."
third complex analysis text[4]: "Gauss defined Theorema Egregium in 1828. He defined principal curvatures to be maximum and minumum values k1 and k2...He then defined Gaussian Curvature K = k1*k2. k1 & k2 are not intrinsic but Gauss discovered K is intrinsic. Pizza has K=0 so we introduce a non-zero k1 forcing k2 to be 0 in order to preserve K because K is locally isometric. For this reason we bend the sides of the pizza to stop the free end from drooping"
But seriously, this Theorema Egregium => Eating Pizza example is straight out of recreational math[1] & is very popular.
standard numerical geom text [2]:"In our everyday life we encounter the Theorema Egregium in a pizzeria..."
another riemann geom text[3]: "There is an interesting real-life application of Theorema Egregium...Notice that when you hold the pizza in one hand, the principal curvature of the crust is much smaller than along the direction of falling toppings."
third complex analysis text[4]: "Gauss defined Theorema Egregium in 1828. He defined principal curvatures to be maximum and minumum values k1 and k2...He then defined Gaussian Curvature K = k1*k2. k1 & k2 are not intrinsic but Gauss discovered K is intrinsic. Pizza has K=0 so we introduce a non-zero k1 forcing k2 to be 0 in order to preserve K because K is locally isometric. For this reason we bend the sides of the pizza to stop the free end from drooping"
[1]http://mathoverflow.net/questions/5450/cocktail-party-math [2]http://tosca.cs.technion.ac.il/book/index.html [3]http://www.damtp.cam.ac.uk/user/pz229/Teaching_files/GR.pdf [4]http://www.amazon.com/Lectures-Complex-Analysis-Contemporary...