Subject: RE: [hackers-il] A joke

From: Chen Shapira <[email-masked]>
Date: Tue, 13 Feb 2001 13:56:39 +0200

> You only need to know the following formula (using i instead of j to 
> confuse the heathens... ;-)
> 
> (e^(i*pi)) = -1
> 
> Therfore:
> hackers(e^(i*pi))[email-masked] = [email-masked]

:-)
 
> You owe the Oracle a Klein bottle.

With beer inside?

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From: Gilad Ben-Yossef <[email-masked]>
Date: Tue, 13 Feb 2001 15:08:42 +0200

>> You owe the Oracle a Klein bottle.

Unfortunatly, a Klein bottle by definition has zero volume, which would 
be quite useless as a beer container.

Even worse, since Klien bottles are one sided surfaces and therefor it's 
inside is also it's outside as it contains itself, meaning I cannot 
drink the zero volume of beer it contains without being inside(outside) 
it...

Even more problematic is the fact that true Klein bottles have the 
quality of being non orientable, which is a bothersome quality to begin 
with, especially if you're drunk from the zero volume of beer you've 
just drank and you're locked into(outside of) your Klein bottle.

All this and I haven't even mentioned the small problem of the of 
attaining 4 dimensions, since true Klein bottle only exists in 4 dimensions.

Yes... I think I'll must have one for my birthday ;-)

http://www.kleinbottle.com/

-- 
Gilad Ben-Yossef <[email-masked]>
http://benyossef.com :: +972(54)756701
"Anything that can go wrong, will go wrong, while interrupts are disabled. "
	-- Murphey's law of kernel programing.

---

From: "Nadav Har'El" <[email-masked]>
Date: Tue, 13 Feb 2001 16:37:50 +0200

> > You owe the Oracle a Klein bottle.

Oops, you fell into his trap :)
A Klein bottle cannot have beer inside, because it doesn't have an inside!

a Klein bottle is a surface like a moebius strip (do you know what that is?)
but with slightly more complicated. Just like a Moebius strip doesn't have an
"up" or "down" side (if you choose a side and walk on it, you'll suddenly find
yourself on the "other" side so the entire surface is actually only one side -
see Escher's beautiful illustration [1]), similarly the Klein bottle (which is
a closed surface) doesn't have an inside or outside - if you find yourself in
what you think is "inside", and walk around, you'll suddenly find yourself
"outside" without crossing the bottle's boundary.

Of course, just like a Moebius strip is a 2D object that needs to be embedded
in 3D space in order to exist, so does a Klein bottle: it cannot be embedded
(without self-intersection) in 3D space and it needs to be in a 4D space.
You can try to make a 3D object which will be a "projection" of a klein
bottle as in [2], but it will intersect itself, just like Escher's 
oebius-strip drawing must intersect itself. See also [3] for a more serious
explanation of what a Klein bottle is.

[1] http://www.math.technion.ac.il/~rl/M.C.Escher/2/escher-moebius.gif
[2] http://www.kleinbottle.com/
    also check out the hillarious http://www.kleinbottle.com/gauss.htm
[3] http://www.math.rochester.edu/misc/klein-bottle.html

-- 
Nadav Har'El                        |     Tuesday, Feb 13 2001, 20 Shevat 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |"Did you sleep well?" "No, I made a
http://nadav.harel.org.il           |couple of mistakes."

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From: Gaal Yahas <[email-masked]>
Date: Tue, 13 Feb 2001 17:27:53 +0200

> be quite useless as a beer container.

Au contraire: a Klein bottle full of beer, in best of Adams "outside
the asylum" tradition, means a universe of beer.

-- 
Gaal Yahas <[email-masked]>

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From: "Nadav Har'El" <[email-masked]>
Date: Tue, 13 Feb 2001 17:43:57 +0200

> the asylum" tradition, means a universe of beer.

Correct me if I'm wrong, but I thought that a Klein bottle was a *surface*,
not a 3D object. As such, it does not have a volume, but rather an area.
Also, the volume inside it (when looking at a 3D immersion) is undefined
because what is "inside" a Klein bottle is undefined!

So I don't see where this talk of either a zero or infinite volume comes from.
You can't just say because something is undefined it must be zero, or must
be infinite. After all, what is 0/0? Is it 0? Is it Infinity? No, it is
neither.

After we decide the volume of the Klein bottle, I suggest we turn our minds
to calculating the area of the second side of the Moebius strip ;)

-- 
Nadav Har'El                        |     Tuesday, Feb 13 2001, 20 Shevat 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |Sign seen in restaurant: We Reserve The
http://nadav.harel.org.il           |Right To Serve Refuse To Anyone!

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From: Moshe Zadka <[email-masked]>
Date: Fri, 16 Feb 2001 21:29:58 +0200 (IST)

On Tue, 13 Feb 2001, "Nadav Har'El" <[email-masked]> wrote:
 
> in 3D space in order to exist, so does a Klein bottle

A Klein bottle is a 2D object which must be embedded in R^4
(just clarifying) 
-- 
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