Greenland looks as big as Africa on most world maps. In reality, Africa is 14 times bigger. And no map can ever get it completely right.

Earlier this month, the UN General Assembly voted 164 to 1 to encourage maps that show countries at their true size. But why was the old map wrong in the first place, and why can't anyone just draw a perfect one? The answer is a beautiful piece of mathematics: Gauss's "remarkable theorem" proves that you can't flatten a sphere without stretching it. In this video we peel an orange, draw a triangle with three right angles, fold a slice of pizza, and catch every map in the act of lying.

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