Beltrami–Klein model
Okay kiddo, imagine you have a big round ball. You can draw a bunch of lines on it to make it look like a map. But the problem is that the ball is 3D and the lines are 2D. So when you look at the map, it looks really distorted and weird.
The Beltrami-Klein model is like taking that map off the ball and stretching it out on a flat surface. But you still want to keep the round shape of the ball in mind. So instead of straight lines, you use curved lines that follow the curves of the ball.
It's kind of like if you drew a doodle on a piece of paper and then crumpled up the paper. The doodle would look all squished and weird. But if you laid the paper flat, you could see the doodle for what it really is.
So now, instead of looking at a weird distorted map, you can look at a flat map that is more true to the actual shape of the ball. This makes it easier for people to understand and work with the map.
Does that make sense?
The Beltrami-Klein model is like taking that map off the ball and stretching it out on a flat surface. But you still want to keep the round shape of the ball in mind. So instead of straight lines, you use curved lines that follow the curves of the ball.
It's kind of like if you drew a doodle on a piece of paper and then crumpled up the paper. The doodle would look all squished and weird. But if you laid the paper flat, you could see the doodle for what it really is.
So now, instead of looking at a weird distorted map, you can look at a flat map that is more true to the actual shape of the ball. This makes it easier for people to understand and work with the map.
Does that make sense?