Triangular decomposition

Alright, kiddo, let me explain what triangular decomposition is in a way you can easily understand.

You know how you love playing with LEGOs and building towers? Let's say we have a big tower made up of lots of smaller LEGO pieces, and we want to take it apart to see how it was built. But there are so many pieces, it's hard to know where to start!

That's where triangular decomposition comes in. It's like breaking down the tower into smaller and more manageable "triangles". We start by looking for smaller groups of LEGOs that fit together in a triangular shape. Once we find one, we take it apart and see how the pieces fit together. Then we move on to the next triangle, and the next, until we've taken apart the entire tower and have a better understanding of how it was built.

Now, in math and computer science, triangular decomposition is a similar process but with shapes and numbers instead of LEGO towers. It's a way to break down more complex geometric shapes and equations into simpler triangular parts that are easier to work with and understand.

So, just like taking apart a LEGO tower, triangular decomposition helps us better understand complicated shapes and equations by breaking them down into smaller, more manageable parts. Pretty cool, huh?