system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What does non-Euclidian mean?
gpt
Euclidean geometry, named after Euclid of ancient Greece,  is the geometry of a perfect, infinite, flat plane.  It's what people learn when they first learn about geometry.  It's a pretty good model for things on the size and scale that humans normally interact with like drawing circles on paper and making houses.

Mathematicians are a restless bunch & they like solving problems just to solve problems.  They've figured out the rules of geometry on balls & donuts and all sorts of weird shapes - these are "Non-Euclidean".  Sometimes they're just interesting mental problems - who really wants to build a house on a donut?  Other shapes, like balls, are more useful - when you're making big enough things, you need to actually pay attention the fact that the earth is round.