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The man with 1,000 klein bottles under his house [video]

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Re: The man with 1,000 klein bottles under his house [video]

#31

Post by tempodox »

thret wrote: post #21
tempodox wrote: post #17

I got one of those Klein bottles from him, and it's really beautifully done. If you are careful, you can even store some liquid or other stuff in it. I wonder if the mathematical original could do that, too.

I suppose I am compelled to get one too. Not that I want one, it's just that I already have his books - and methinks he deserves a little extra money for this video.

It's hard for me to resist “math you can touch” :) And although it's “only” in 3 dimensions, the sheer craftsmanship is a feat in itself.

Re: The man with 1,000 klein bottles under his house [video]

#32

Post by talideon »

bambax wrote: post #5

Real life Gyro Gearloose!!! In the next video he talks about how a Klein bottle is made, and how, contrary to a bottle, it has no edge. I'm not sure I understand why a bottle "has to" have an edge? Surely it's possible to make a bottle with no edge? For example, if one takes a sphere and progressively turns it into a bowl (by punching into it), and then makes the bowl deeper, it still has just one surface and no edge…

The rim of your bowl is the edge: it's a point where the curvature changes suddenly. But that's not the important thing: the important thing is that not only is there only no edge, but only one surface.

Let's talk topology for a bit.

A manifold can be thought of as essentially a flat and infinitely thin sheet. If you have a spherical manifold (and your bowl would be a spherical manifold), it has two surfaces: one on the inside and another on the outside. Deforming the manifold doesn't change this.

The thing about a Klein bottle (and a Moebius strip) is that it only has one continuous surface, the difference between a Moebius strip and a Klein bottle is that the latter is a single surface with no edge whereas the former is a single surface with one edge, unlike the sphere (or your bowl), which has two surfaces and no edge.

So what's important here is the number of sides it has, not really that it has no edge. The lack of an edge is really only what separates a Moebius strip from Klein bottle.

Re: The man with 1,000 klein bottles under his house [video]

#33

Post by hedgew »

harel wrote: post #30

What would be a practical use for such a feat of inter dimension glass containerism?

Its practical uses are both guaranteed and finite!

>You can convert your Acme Klein Bottle into an astonishing amount of energy, over 1023 ergs! Enough to power a small city for years. To get you started, we'll supply the necessary equation for free.

>At any time -- day or night -- you can easily check on the Euler Characteristic of your Acme Klein Bottle. Just add the number of vertices to the number of faces, then subtract the number of edges. So simple, even a grad student can do it!

http://www.kleinbottle.com/why_acme.htm

Re: The man with 1,000 klein bottles under his house [video]

#36

Post by jay-saint »

Check out his job postings for his Acme Klein Bottle company http://www.kleinbottle.com/jobs.html

My favorite: PENTIUM PROCESSOR. Must know all pentium processes, including preprocessing, postprocessing, and past-pluperfect processing. Ideal candidate pent up at the Pentagon, penthouse, or penitentiary. Pays pennies. Penurious benefits include Pension, Pencil. Pentel, Pentax, and Pentaflex. Write to pensive@kleinbottle.con

Re: The man with 1,000 klein bottles under his house [video]

#38

Post by raldi »

bambax wrote: post #5

Real life Gyro Gearloose!!! In the next video he talks about how a Klein bottle is made, and how, contrary to a bottle, it has no edge. I'm not sure I understand why a bottle "has to" have an edge? Surely it's possible to make a bottle with no edge? For example, if one takes a sphere and progressively turns it into a bowl (by punching into it), and then makes the bowl deeper, it still has just one surface and no edge…

I could paint the inside of your surface red and the outside blue (where by "inside" I mean the part you've trapped air in). That's not the case with Cliff's bottles.

Re: The man with 1,000 klein bottles under his house [video]

#39

Post by raldi »

tempodox wrote: post #17

I got one of those Klein bottles from him, and it's really beautifully done. If you are careful, you can even store some liquid or other stuff in it. I wonder if the mathematical original could do that, too.

You're not really storing the liquid in it; you're storing the liquid on it.

Re: The man with 1,000 klein bottles under his house [video]

#40

Post by JoeAltmaier »

raldi wrote: post #39
tempodox wrote: post #17

I got one of those Klein bottles from him, and it's really beautifully done. If you are careful, you can even store some liquid or other stuff in it. I wonder if the mathematical original could do that, too.

You're not really storing the liquid in it; you're storing the liquid on it.

True of an ordinary bottle too, which is topographically the same as a plate.
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