ELI5: Explain Like I'm 5

non-euclidean geometry

Non-Euclidean geometry is a type of math that is different from what we usually learn in school. In Euclidean geometry (the type of math we usually learn in school), the rules say that all angles have the same measure and all straight lines go on forever in both directions. In non-Euclidean geometry, the rules are different. For example, in some non-Euclidean geometry, the angles of a triangle can add up to more or less than 180°, and straight lines can curve in certain ways. Non-Euclidean geometry can be used to understand the shapes of some things in nature that don't follow the rules of Euclidean geometry, like the surface of the Earth.