# An Intro to Manifolds

20 min readApr 11, 2023

Euclidean space is the natural environment for Calculus, but manifolds allow us to extend Calculus to curved spaces.

We’ve been working with manifolds since the first article in this series, but we didn’t say we were working with manifolds until *An Intro to Differential Geometry*. Even then, we only said that a manifold had to be locally Euclidean, but that’s only one of three requirements we want of manifolds.