Net of a Sphere

Transcript

Net of a SphereSphere is a 3-dimensional object shaped like a ball. Every point on the surface is the same distance from the center. The net of a sphere is mathematically impossible! The Explanation: A flat piece of paper has zero curvature. A sphere has continuous, positive curvature in all directions. You cannot bend a flat surface to perfectly match a curved surface without stretching it, tearing it, or wrinkling it. (Try wrapping a basketball in a single sheet of wrapping paper—it always wrinkles!). This is actually a famous mathematical rule called Gauss's Theorema Egregium, and it's the exact reason why flat maps of the Earth always have distorted countries!