If you don’t know what that means, don’t worry neither do most people. But let me break it down for ya:

A Riemannian manifold is basically just a fancy way of saying “a curved space with some rules.” And when we say “curved,” we mean like if you were to take a piece of paper and crumple it up into a ball that’s what we’re talking about. But instead of using our hands, we use math!

So geodesics. A geodesic is essentially the shortest distance between two points on this curved space. It’s like if you were trying to walk from one end of a crumpled-up piece of paper to another you would want to follow the path that takes the least amount of time (or, in math terms, the path with the smallest length).

Now, how do we actually find these geodesics? Well, that’s where solving the geodesic equations comes in. These are a set of differential equations that help us figure out which paths on our curved space are the shortest (or, more technically speaking, they give us the “normal” or “straightest” path between two points).

So how do we solve these equations? We have computers for that. And if you really want to impress your friends at a dinner party (or just sound like a math nerd), you can always whip out some fancy notation and start talking about things like “Riemannian metrics” and “Christoffel symbols.”

But let’s be real most of us don’t have time for that. We want to understand these concepts in plain English, without all the math jargon. And that’s what we’re here for! So if you ever find yourself lost in a sea of equations and symbols, just remember: at its core, solving geodesic equations is really just about finding the shortest path between two points on a curved space.

And hey who knows? Maybe one day you’ll be able to impress your friends with some fancy math talk! But for now, let’s keep it simple and enjoy the beauty of these curvy spaces we call home.