Nash embedding theorem
Imagine you have a bunch of dots on a piece of paper. Some dots are closer together and some dots are farther apart. The Nash embedding theorem is like a magic tool that can take these dots and stretch, twist, or turn them in such a way that they look like they are sitting on a flat surface even though they might have been on a bumpy or curved surface before.
This is useful when mathematicians want to study shapes that are harder to understand when they are bumpy or curved. By using the Nash embedding theorem, they can make these shapes flat and easier to understand. It's like when you want to take a picture of a dog, but the ground is bumpy and uneven. By asking the dog to sit on a flat piece of cardboard, the picture turns out much clearer and easier to see.
The Nash embedding theorem was named after its discoverer, mathematician John Forbes Nash Jr. who was famous for his work in game theory and differential geometry. This theorem is often used to help mathematicians understand things like patterns in the sky, how fluids move through pipes, and how diseases spread through populations.
This is useful when mathematicians want to study shapes that are harder to understand when they are bumpy or curved. By using the Nash embedding theorem, they can make these shapes flat and easier to understand. It's like when you want to take a picture of a dog, but the ground is bumpy and uneven. By asking the dog to sit on a flat piece of cardboard, the picture turns out much clearer and easier to see.
The Nash embedding theorem was named after its discoverer, mathematician John Forbes Nash Jr. who was famous for his work in game theory and differential geometry. This theorem is often used to help mathematicians understand things like patterns in the sky, how fluids move through pipes, and how diseases spread through populations.