An Intro to Manifolds

Joseph Mellor
20 min readApr 11

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

This is stop 18 on the Road to Quantum Mechanics. I made a little guy out of these locally Euclidean maps on accident.

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.

Joseph Mellor

BS in Physics, Math, and CS with a minor in High-Performance Computing. You can find all my articles at