The concept of a Klein bottle was first described in 1882 by the German mathematician Felix klein.
A Klein bottle is a more complex and goofy looking version of the same concept because the neck of the bottle disappears into itself in such a way that there is no outside or inside, just one continuous surface.
In simple explaination,"If you want to paint the inside blue and the outside red, you would start painting the outside of the base red, and then paint up the neck, and then suddenly you would find yourself on the inside of the bottle!"
The outside of the neck fluidly becomes the inside of the base.
This is why they have to be computer models or blown glass; it's kind of difficult to make something that goes through itself, so the choices for building it are limited.
Can we make or use a klein bottle in 3 dimension?
A recreation of a glass Klein bottle is obviously a 3d object. You can hold it.
However, the concept of a Klein bottle is very clearly a four dimensional object.
The Klein bottle was invented as a 4d-take on the 3d “Möbius strip,” eliminating edges from the equation as well.
If you don’t know what a Möbius strip is, take a long rectangular piece of paper, turn one end over so there’s a fold, then tape the ends together. You can run your finger along the surface of the Möbius strip, and it will magically cross over to the other “side.” Same with the edges.
So now you might got an idea regarding Klein bottle but can we able to use it in our practical life?
Within mathematics, it’s a good example of a non-orientable closed manifold which makes it very practical when you’re showing the wonders of math to kids or teaching a course in algebraic topology.
This is "impractical" for educationists who rely absolutely on the complete independence of these directions while performing calculations that render their mathematical computations invariant.
Anyone can observe visually, that the human hip socket is the self re-retry point of an anatomical Klein Bottle construct. The human eye ball and socket as well as the human shoulders have a similar visible Klein Bottle form. Our eyes, shoulders and hips are very practical in their usefulness in redirecting momentum within the human body. So practical, in fact, that it gives a vast capacity for varying our momentum in many directions. In fact you could not read this if it were not for the practical value of the Klein Bottle form of the human eye, and their ability to move in 3D space.
Math behind the fact:
Mathematicians like to classify surfaces (meaning they try to understand what are all the possible 2-dimensional surfaces). We actually now know the answer to this question. If we were living 500 years ago and didn’t know the shape of the surface of the earth, then knowing all possible surfaces would at least limit the possibilities!.
But we still don’t know what all possible 3-dimensional objects (called manifolds) look like, and we do not know which one of those objects our 3-dimensional universe is, either!.