# What is the exponential map?

I am well versed in Calculus but I have never taken a differential geometry course. I am trying to understand what the exponential map is, with the main purpose to approximate a geodesic line on an elliptical manifold.

I have read a couple of sites that try to describe it, but doing depth first search on every single term I encounter that I can't recognize is not very efficient.

Can someone give an intuitive explanation of what the exponential map is?

• So if I want to approximate the goedesic conatining 2 points $A$ and $B$ then all I do is project the straight line containing the 2 points onto the ellipse, but there are multiple projections possible, how do i pick one that approximates the geodesic? – Makogan Dec 4 '17 at 23:56