Berry connection and curvature
Have you ever seen a berry growing on a vine or bush? Well, imagine that vine is like a long, twisty piece of spaghetti noodle. When we talk about "berry connection," we're talking about how that spaghetti noodle (which is really a type of surface called a manifold) is connected to the berry.
Now, when we talk about "curvature," we're talking about how bent or curved that spaghetti noodle is. You see, if you try to bend a spaghetti noodle too much, it will break, just like how if you try to bend your finger too far back, it will hurt.
But sometimes, it's important to know just how curved that spaghetti noodle is, or how much it's bending. This is where the idea of curvature comes in.
Did that make sense? Basically, we're looking at how connected the berry is to the surface it's growing on, and how much that surface is bending.
Now, when we talk about "curvature," we're talking about how bent or curved that spaghetti noodle is. You see, if you try to bend a spaghetti noodle too much, it will break, just like how if you try to bend your finger too far back, it will hurt.
But sometimes, it's important to know just how curved that spaghetti noodle is, or how much it's bending. This is where the idea of curvature comes in.
Did that make sense? Basically, we're looking at how connected the berry is to the surface it's growing on, and how much that surface is bending.