Many of the ideas in curved-surface math (which is technically called “differential geometry”) first originated when people tried to draw accurate maps of the Earth’s surface. Maps are drawings of pieces of the surface of the Earth - which is approximately spherical - on flat pieces of paper. But we know that spheres and flat pieces of paper aren’t isometric, so you can’t transform one into the other without stretching. What consequences do you think this might have for the shapes of countries on a map of the world? It helps to visualize this problem if you carefully peel a mandarin orange, and then try to lay the strips down flat on a table.