What is the differences and what are the uses of non Euclidean geometry in the real world if there are any?
In: Mathematics
Euclidean geometry is the geometry that you learn in grade school: the rules are the same regardless of where you move/rotate yourself in a Euclidean space. Distances between points are simply the length of the line segment connecting those points, and so on.
Non-Euclidean geometry is anything that breaks those rules. (Portal is a good example, if you’ve ever played it: the distance between two points depends on whether you go through a portal or walk, and it’s possible to get back to where you started even if you never turned around by creating infinite loops with portals, etc.)
In the real world, the surface of Earth is actually non-Euclidean: if you start at the south pole, go 100 feet north, 100 feet east, and 100 feet south, you’ll end up back where you started (Euclidean geometry demands that you end up 100 feet east of where you started). I live in Colorado, and even though it’s a “rectangle,” the northern border is about 26 miles shorter than the southern, due to the curvature of Earth. Higher physics also involves non-Euclidean geometry, in the form of wormholes and such.
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