Kellogg's theorem

Kellogg's Theorem is a mathematical rule that says if you have a shape and you want to find out if it's a certain type of shape (like a circle), you can look at how it jiggles around when you push on it.

Imagine you are trying to find out if a coin is actually a circle. If you push on the edges of the coin, even just a little bit, it will still be nice and round. This means that the coin is a circle (or very, very close to being a circle).

On the other hand, if you have a square and you push on one of the sides, the shape will change pretty quickly. This means that the square is not a circle.

Kellogg's Theorem tells us that we can use this idea of jiggling shapes around to figure out all kinds of things about them. It can help us find out if a shape is symmetrical or if it has holes in it, for example. It's a really useful tool for mathematicians and scientists who study shapes and how they behave.