Homeotopy

Okay kiddo, have you ever seen a piece of clay before? Imagine that you have a piece of clay and you can mold it into any shape you want. If you squish it, stretch it, and press it, you can make it look like a lot of different things, right?

Well, this idea of changing the shape of things is kind of like what happens with homeotopy! Homeotopy is a big word that means "changing the shape of something without cutting it".

It's like if you have a rubber band and you stretch it out as long as it can go. If you then turn it around and twist it a bit, it will look like a new shape, even though it's still the same rubber band! That's kind of like homeotopy.

With homeotopy, mathematicians can "bend" or "twist" mathematical shapes like circles, squares, and triangles without cutting them or changing their size. They can do this bending and twisting in lots of different ways, like stretching, twisting, or moving points around.

Homeotopy is a really cool tool for mathematicians because it helps them understand how shapes and geometrical figures can be related to each other. It’s a bit like playing with clay or playdough but all in your head!