Why World Maps Are Wrong?
4 Minutes
Why world maps are distorted explained for students using curvature and Gauss's remarkable theorem. A Tamil maths and science lesson.
- Bending a pizza slice to explain Gauss's remarkable theorem
- Comparing curvatures of flat paper, a cylinder, and an orange peel
- Why spherical Earth gets distorted when projected onto a flat map
What this lesson teaches
World maps show country sizes incorrectly because a spherical surface like Earth cannot be flattened onto a flat sheet without distorting shapes and sizes. This geometric rule comes from a mathematical principle discovered by Gauss called the remarkable theorem, which describes the curvature of surfaces.
How surface curvature is calculated
The curvature of a surface at any point is found by choosing two different directions and multiplying their individual curvatures together. A flat sheet of paper has zero curvature in both directions, so zero multiplied by zero gives an overall curvature of zero. When that flat paper is rolled into the shape of a cylinder, one direction has positive curvature while the other direction has zero curvature. Multiplying positive curvature by zero still equals zero, proving that bending a flat surface does not change its curvature.
The orange peel experiment
- An orange cut in half has a peel with positive curvature in both chosen directions.
- Multiplying positive curvature by positive curvature gives the sphere an overall positive curvature.
- Because a flat surface has zero curvature, an orange peel cannot be pressed flat into a perfect circle without leaving gaps.
- A flat gift-wrapping sheet similarly cannot smoothly cover a round ball without wrinkling and bunching up.
How mapmakers project the globe
Earth is a sphere with positive curvature at every point, while a wall map or paper map has zero curvature. Because a surface with positive curvature can never be converted into a surface with zero curvature, a flat map cannot represent the globe exactly. To force the spherical surface onto a flat page, mapmakers stretch the top and bottom regions of Earth larger than their normal size and shrink the middle sections smaller than their normal size.
Distortions seen on world maps
- Greenland appears much larger than China on a flat map, even though China is actually four times larger in real life.
- India looks smaller on a flat world map than its actual size on the physical globe.
- Bending a floppy slice of pizza into a U shape relies on this same curvature rule to keep heavy toppings from falling off.