What is Non-Euclidean Geometry?
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A long time ago a guy named Euclid basically defined a set of “rules” for geometry, most of which seem fairly obvious at first, like, “there is exactly one way to draw a straight line between any two points,” or “straight lines go on forever”.
However, it turns out these rules are only true because we’re used to doing geometry on flat planes or 3d space. If you get a little creative with how you define space, these rules don’t always hold anymore, at which point we call your type of geometry “non-euclidean”.
One really easy example is the surface of the Earth! The Earth is a sphere, and so we can do things on it that we can’t do in a flat plane. For example, if you started walking in a perfectly straight line, you’d eventually circle the whole planet and arrive back where you started, which violates the rule that straight lines must go on forever. Also, there is no longer always exactly one way to draw a straight line between two points; if you start at the north pole, for example, you could walk in a straight line in any direction you want and you would still end up at the south pole eventually.
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