Lie sphere geometry

Lie sphere geometry is like playing with balls, but they aren't quite normal balls. Instead, they are like squishy balls that can change shape and size, but they always stay round. Imagine you have a bunch of these squishy balls and you want to see how they fit together in space. That's what Lie sphere geometry is all about.

Now, let's say you have two of these squishy balls, and they are touching each other. You might notice that there is a line where they touch, right? Well, in Lie sphere geometry, that line is called a circle. And just like how you can draw a line on paper, you can draw a circle in Lie sphere geometry.

But it gets more exciting. Let's say you want to see how three of these squishy balls fit together. You might arrange them so that they touch each other, but this time they touch at three different points. In Lie sphere geometry, those three points where the balls touch are called a triple intersection. And just like how you can draw a circle in Lie sphere geometry, you can draw a triple intersection too!

All of this might sound like fun and games, but Lie sphere geometry has some serious uses too. It is used in physics, engineering, and even computer science to solve problems related to space and shape. So next time you play with a ball, remember, you might just be practicing Lie sphere geometry!