Mazur–Ulam theorem
The Mazur-Ulam Theorem is a mathematical idea that says that if you have two points on a flat surface, there is a transformation (a way to change the points around) that will keep the distance between them the same.
Think of it like this: Imagine you have two stickers on a piece of paper. You could move those stickers around and twist the paper all you want, but the distance between them would stay the same. That's what the Mazur-Ulam Theorem is talking about, but with a lot more math involved.
It's a really important idea in geometry and helps us understand how shapes can be changed without losing certain properties, like distance or angles. It's also pretty cool because it helps us think about how different shapes and spaces can be related to each other.
Think of it like this: Imagine you have two stickers on a piece of paper. You could move those stickers around and twist the paper all you want, but the distance between them would stay the same. That's what the Mazur-Ulam Theorem is talking about, but with a lot more math involved.
It's a really important idea in geometry and helps us understand how shapes can be changed without losing certain properties, like distance or angles. It's also pretty cool because it helps us think about how different shapes and spaces can be related to each other.