Spherical basis

Imagine you have a big ball, like a giant beach ball. This ball is special because you can use it to describe things that happen all around it.

Now imagine you have a little pencil and a piece of paper. You can use that pencil and paper to draw some lines and shapes on it. But what if you want to draw something that happens all around the ball, like a big circle that goes all the way around it? How do you draw that on a flat piece of paper?

Well, that's where the spherical basis comes in. A spherical basis is like a special set of rulers and pencils that helps you draw things on the ball itself instead of on a flat piece of paper.

It works by breaking up the ball into special little pieces, kind of like a puzzle. Each piece is called a "spherical harmonic" and it's shaped a bit like a cookie. These spherical harmonics are important because they help you measure things on the ball, like how strong a certain force is at different points.

So if you have a problem that involves things happening all around the ball, you can use the spherical basis to help you solve it. The spherical basis makes it easier to measure and compare things that happen in different parts of the ball, even though the ball is round and not flat like a piece of paper.

In short, a spherical basis is a way of breaking up a big round ball into little pieces so that you can measure and describe things that happen all around it.