Geodesics on a triaxial ellipsoid

Hey there kiddo! Have you ever seen a ball or a globe? Well what if I told you there's a special type of path you can draw on it that's actually the shortest distance between two points? That's what we call a geodesic!

Now imagine a special kind of ball that isn't perfectly round like a globe. It's called a triaxial ellipsoid and it's shaped kind of like an egg or a football. On this type of ball, the geodesics aren't straight lines like on a globe. They follow a curve that's the shortest distance between two points on the surface.

Think of it like tracing a path on the ball with a pen. You want to start at point A and end at point B, but you want to take the shortest path possible. The curve you draw with the pen, without lifting it off the ball, is the geodesic.

Now, because the triaxial ellipsoid has different lengths for its three axes, the geodesics aren't all the same. Some curve more than others depending on the orientation of the ball. But they all have something in common: they are the shortest distances between two points on the surface of the triaxial ellipsoid!