Level Curves & Contours

Open a hiking map and you'll see squiggly closed loops labeled with numbers like 1000, 1200, 1400. Those are contour lines — and they're pure multivariable calculus. Each loop connects all the points at the SAME elevation. Where the loops bunch together, the slope is steep; where they spread apart, it's gentle. With this trick a 3D mountain collapses onto a flat sheet of paper without losing a thing.