Does non-Euclidian geometries induce euclidian geometry locally?

71 Views Asked by At

This is essentially a soft question.

We know the world is a sphere, following spherical geometry, yet at local levels, we can observe euclidian geometry. This brings me to my question,

Does non-Euclidian geometries induce euclidian geometry locally?

1

There are 1 best solutions below

4
On BEST ANSWER

I'm not sure that I'd say non-Euclidean geometries induce Euclidean geometry locally, but I'm not a geometer. The key idea behind what you observe regarding spheres is that any manifold (like a sphere) is locally homeomorphic to Euclidean space.