Möbius transform

Imagine you have a piece of paper with a drawing on it. A möbius transform is when you take that piece of paper and twist it, fold it, or stretch it in a certain way so that the drawing on it looks different.

Now, let's make it more specific. A möbius transform is a type of mathematical transformation (like addition or multiplication) that can change the shape of certain objects in a special way. It's kind of like a magic trick for shapes!

To understand how it works, imagine drawing a circle on your piece of paper. Now imagine putting a piece of string around the circle and tying it so that it makes a loop. If you twist the loop and then untie it, the circle will look like it's been distorted into a different shape.

That's kind of like what a möbius transform does. It takes a shape like a circle, twists it or stretches it in a certain way, and then lets it go so that it looks different. The cool thing about möbius transforms is that they work for all kinds of shapes, not just circles.

So there you have it! A möbius transform is a cool math thing that can transform shapes in a magical way.