# Klein Bottles are Awesome but do you know how to Fill a Klein Bottle???

### Can a Klein Bottle be filled with Water???

How To Fill a Klein Bottle The Easy Way

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So I got my new Klein Bottle but now how do I fill the Klein Bottle.

In this video I show how to fill a Klein Bottle with Water with a simple method we used to fill glass barometers.

https://www.youtube.com/watch?v=bd2YiD9JXsk

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### Liquid Filled Klein Bottles

### Tiny Klein Bottle filled with Water

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From www.Kleinbottle.com

A true Klein Bottle lives in 4-dimensions. But every tiny patch of the Klein Bottle is 2-dimensional. In this sense, a Klein Bottle is a 2-dimensional manifold which can only exist in 4-dimensions!

Alas, our universe has only 3 spatial dimensions, so even Acme’s dedicated engineers can’t make a true Klein Bottle.

A photograph of a stapler is a 2-dimensional immersion of a 3-dimensional stapler. The true stapler has been flattened into the flatland of the photo. In the same way, our glass Klein Bottles are 3-D immersions of the 4-D Klein Bottle. Acme’s Klein Bottle is a 3-dimensional photograph of a “true” Klein Bottle.

A Klein Bottle cannot be embedded in 3 dimensions, but you can immerse it in 3-D. (An immersion may have self-intersections; Embeddings have no self-intersections. Neither an embedding nor an immersion has folds or cusps.)

We represent a Klein Bottle in glass by stretching the neck of a bottle through its side and joining its end to a hole in the base. Except at the side-connection (the nexus), this properly shows the shape of a 4-D Klein Bottle. And except at the nexus, any small patch follows the laws of 2-dimensional Euclidean geometry.

Contrast this with a corked bottle — say, a wine bottle. It has two sides: inside and outside. You can’t get from one to the other without drilling a hole or popping the top. Once uncorked, it has a lip which separates the inside from the outside. If you make the glass arbitrarily thin, that lip won’t go away. It’ll become more prominent. The lip divides one side of the bottle from the other. So an uncorked bottle is topologically the same as a disc … it has two sides, separated by a boundary — an edge.

But a Klein Bottle does not have an edge. It’s boundary-free, and an ant can walk along the entire surface without ever crossing an edge. This is true of both theoretical Klein Bottles and our glass ones. And so, a Klein Bottle is one-sided.

A Klein Bottle has one hole. This, in turn, causes it to have one handle. The genus number of an object is the number of holes (well, it’s more subtle than that, but I’m not allowed to tell you why). Other genus-1 objects include innertubes, bagels, wedding rings, and teacups. A wine bottle has no holes and so is genus 0

2×2 Tutorial Finished!

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