Birkhoff–Grothendieck theorem
The Birkhoff-Grothendieck Theorem says that every convex polygon, which is a shape with straight sides and no holes, can be tiled by triangles.
Imagine you have a bunch of tiles that are shaped like triangles and you want to cover a polygon, which is essentially a shape with straight sides like a square or rectangle, with these tiles. If the polygon is convex, which means it doesn't have any holes and has all of its angles pointing outwards, then it is possible to cover the entire polygon perfectly with these tiles without leaving any gaps or overlaps.
Think of it like trying to put puzzle pieces together - just as you have to fit shapes together to form a complete image, you can use triangles to fill in the entire convex polygon in a puzzle-like way.
This theorem was first discovered by two mathematicians, Birkhoff and Grothendieck, and it has a lot of practical applications in areas like computer graphics, where you may need to use triangles to create 3D images or models.
Imagine you have a bunch of tiles that are shaped like triangles and you want to cover a polygon, which is essentially a shape with straight sides like a square or rectangle, with these tiles. If the polygon is convex, which means it doesn't have any holes and has all of its angles pointing outwards, then it is possible to cover the entire polygon perfectly with these tiles without leaving any gaps or overlaps.
Think of it like trying to put puzzle pieces together - just as you have to fit shapes together to form a complete image, you can use triangles to fill in the entire convex polygon in a puzzle-like way.
This theorem was first discovered by two mathematicians, Birkhoff and Grothendieck, and it has a lot of practical applications in areas like computer graphics, where you may need to use triangles to create 3D images or models.