Klein Bottle (Navigation on weird worlds)
 

Back when I was discussing coord systems for navigating on weird shaped
worlds, someone pointed out that I could actually buy a Kleins bottle
from a company called "ACME Kleins Bottles" so I ordered one. They
also have a great thing called "The Mug of Tantalus" which is a blown
glass beer mug with a siphon built into the handle. You can fill the
mug about halfway with no problem but if you go any higher ALL the
liquid drains out via the siphon. Of course, I bought one for a beer
drinking friend.
The proprieter who refers to himself as "Chief Klein's Bottle Washer"
sent it along with terrible puns and inside math jokes and
certification of zero volume. I e-mailed back a few of my own and his
name started to sound familiar. It turns out that he is Cliff Stoll
who wrote several books about the internet, was briefly famous for
catching some criminal hackers and wrote an article in Sci Am. about
the Curta calculator.
The Klein Bottle is not as cool as I thought it would be primarily
because none of my friends know what it is so they do not appreciate it.

Klein Bottle (Navigation on weird worlds)
 

You would probably enjoy making your own mobius strip. Much cheaper and
easier to understand. You'll usually get a light going on expression when
you trace around it and show someone that it only has one surface.

--
Roger Long

Klein Bottle (Navigation on weird worlds)
 

Roger Long wrote:
You would probably enjoy making your own mobius strip. Much cheaper and
easier to understand. You'll usually get a light going on expression when
you trace around it and show someone that it only has one surface.

--
Roger Long

When I was 13, I was obsessed with Mobius strips in every fashion, I
made them from paper, plastic. soldered metal, etc. I tried to make a
Klein Bottle without the "junction" by joining the edge(s) of a mobius
strip with strips and fastening them together, tried to make part of a
Projective Plane, etc. My kids do not share this obsession.

Klein Bottle (Navigation on weird worlds)
 

"Roger Long" wrote in
:

You would probably enjoy making your own mobius strip. Much cheaper
and easier to understand. You'll usually get a light going on
expression when you trace around it and show someone that it only has
one surface.


"It only has one edge, but does it have only one PLANE?!" - A Einstein,
genius.

Klein Bottle (Navigation on weird worlds)
 

"Frogwatch" wrote in message
ups.com...

Roger Long wrote:
You would probably enjoy making your own mobius strip. Much cheaper and
easier to understand. You'll usually get a light going on expression
when
you trace around it and show someone that it only has one surface.

--
Roger Long

When I was 13, I was obsessed with Mobius strips in every fashion, I
made them from paper, plastic. soldered metal, etc. I tried to make a
Klein Bottle without the "junction" by joining the edge(s) of a mobius
strip with strips and fastening them together, tried to make part of a
Projective Plane, etc. My kids do not share this obsession.


Any Mobius strip you can build has two surfaces, not one. Don't forget to
include the edge (which interestingly it has only one).

The only closed solid with one surface where there is a "hole" in the center
is a torus.


So if one takes a multiple pulley system with a mechanical advatange of 8
and replaces the line with straps sewn to be mobius strips does the
mechanical advantage become 16 or 64?


Gilligan

Klein Bottle (Navigation on weird worlds)
 

Gilligan wrote:

Any Mobius strip you can build has two surfaces, not one. Don't
forget to include the edge (which interestingly it has only one).


But who's counting?

If you call the edge a surface, sure it's got two surfaces. If it's an edge
and not a surface than it only has one surface.

--
Roger Long

Klein Bottle (Navigation on weird worlds)
 

NERD ALERT !!! NERD ALERT !!!!
NERD ALERT !!!!



"Frogwatch" wrote in message
ups.com...

Roger Long wrote:
You would probably enjoy making your own mobius strip.
Much cheaper and
easier to understand. You'll usually get a light going
on expression when
you trace around it and show someone that it only has
one surface.

--
Roger Long

When I was 13, I was obsessed with Mobius strips in every
fashion, I
made them from paper, plastic. soldered metal, etc. I
tried to make a
Klein Bottle without the "junction" by joining the edge(s)
of a mobius
strip with strips and fastening them together, tried to
make part of a
Projective Plane, etc. My kids do not share this
obsession.

Klein Bottle (Navigation on weird worlds)
 

Frogwatch wrote:
Back when I was discussing coord systems for navigating on weird shaped
worlds, someone pointed out that I could actually buy a Kleins bottle
from a company called "ACME Kleins Bottles" so I ordered one. They
also have a great thing called "The Mug of Tantalus" which is a blown
glass beer mug with a siphon built into the handle. You can fill the
mug about halfway with no problem but if you go any higher ALL the
liquid drains out via the siphon. Of course, I bought one for a beer
drinking friend.
The proprieter who refers to himself as "Chief Klein's Bottle Washer"
sent it along with terrible puns and inside math jokes and
certification of zero volume. I e-mailed back a few of my own and his
name started to sound familiar. It turns out that he is Cliff Stoll
who wrote several books about the internet, was briefly famous for
catching some criminal hackers and wrote an article in Sci Am. about
the Curta calculator.
The Klein Bottle is not as cool as I thought it would be primarily
because none of my friends know what it is so they do not appreciate it.

Sure, I remember Cliff Stoll. Thx for the update. I think I'll get
myself one of them there Klein bottles.

Klein Bottle (Navigation on weird worlds)
 

"Frogwatch" wrote in message
ups.com...

Roger Long wrote:
You would probably enjoy making your own mobius strip. Much cheaper and
easier to understand. You'll usually get a light going on expression
when
you trace around it and show someone that it only has one surface.

--
Roger Long

When I was 13, I was obsessed with Mobius strips in every fashion, I
made them from paper, plastic. soldered metal, etc. I tried to make a
Klein Bottle without the "junction" by joining the edge(s) of a mobius
strip with strips and fastening them together, tried to make part of a
Projective Plane, etc. My kids do not share this obsession.


My son wasn't into this stuff either and it really bothered me until his
mother pointed out that I should wait till he was older than 18 months. I
faced reality at that point, and put away the Marx Brothers movies, kid
science books, .22 caliber rifle, and assorted fishing poles for a later
date. Now, at 212 months, he's interested in every damned thing.

Be patient.

Klein Bottle (Navigation on weird worlds)
 

"Short Wave Sportfishing" wrote in message
...
On 11 Dec 2006 09:13:54 -0800, "Frogwatch"
wrote:

The Klein Bottle is not as cool as I thought it would be primarily
because none of my friends know what it is so they do not appreciate it

It's not as cool as you thought it was going to be because if can't
exist in a 3D world.


*YOU* shouldn't exist in a 3D world, and yet, you do.

Klein Bottle (Navigation on weird worlds)
 

Frogwatch wrote:
Roger Long wrote:

I tried to make a
Klein Bottle without the "junction" by joining the edge(s) of a mobius
strip with strips and fastening them together, tried to make part of a
Projective Plane, etc. My kids do not share this obsession.

My wife has several empty Klein bottles.

Why would your kids want to wear Calvin Klein Obession ?

Joe

Klein Bottle (Navigation on weird worlds)
 

Gene Kearns wrote:
rily
because none of my friends know what it is so they do not appreciate it.

Sure, I remember Cliff Stoll. Thx for the update. I think I'll get
myself one of them there Klein bottles.

Actually, I suspect the Klein cap is more practical.....
http://www.kleinbottle.com/klein_bottle_hats.htm

Their products come with an unrivaled warranty...
http://www.kleinbottle.com/guarantee.htm

Is it really a Klein hat if you can get your head into it?

Klein Bottle (Navigation on weird worlds)
 

Paul Cassel wrote:
Gene Kearns wrote:
rily
because none of my friends know what it is so they do not appreciate
it.

Sure, I remember Cliff Stoll. Thx for the update. I think I'll get
myself one of them there Klein bottles.

Actually, I suspect the Klein cap is more practical.....
http://www.kleinbottle.com/klein_bottle_hats.htm

Their products come with an unrivaled warranty...
http://www.kleinbottle.com/guarantee.htm

Is it really a Klein hat if you can get your head into it?

You have to be able to get your head around it.

Klein Bottle (Navigation on weird worlds)
 

Paul Cassel wrote:
Gene Kearns wrote:
rily

because none of my friends know what it is so they do not appreciate
it.

Sure, I remember Cliff Stoll. Thx for the update. I think I'll get
myself one of them there Klein bottles.


Actually, I suspect the Klein cap is more practical.....
http://www.kleinbottle.com/klein_bottle_hats.htm

Their products come with an unrivaled warranty...
http://www.kleinbottle.com/guarantee.htm


Is it really a Klein hat if you can get your head into it?

If you like guarantees...try this one...
http://www.tilley.com/guarantee.asp

Klein Bottle (Navigation on weird worlds)
 

Frogwatch wrote:

Back when I was discussing coord systems for navigating on weird shaped
worlds,

In a really weird shaped world, if you would navigate long
enough you return to your original position and find your
friends have turned to their mirror images. That would
happen to 2-dimensional creatures travelling a (transparent)
mobius band.
http://plus.maths.org/issue26/featur...ndex-gifd.html

someone pointed out that I could actually buy a Kleins bottle
from a company called "ACME Kleins Bottles" so I ordered one. They
also have a great thing called "The Mug of Tantalus" which is a blown
glass beer mug with a siphon built into the handle. You can fill the
mug about halfway with no problem but if you go any higher ALL the
liquid drains out via the siphon. Of course, I bought one for a beer
drinking friend.

A variation of The Mug of Tantalus is known as
Pyhthagoran Mug of Justice.
http://www.mlahanas.de/Greeks/InventionsP.htm
Pythagoras invented this as he thought his friends were
drinkin all too much. They still make those for tourists to
buy - out of clay, as was the original - on Pyhtagoras' home
island Samos in Greek.

The Klein Bottle is not as cool as I thought it would be primarily
because none of my friends know what it is so they do not appreciate it.

Btw, the story in
http://plus.maths.org/issue26/featur...ndex-gifd.html
suggests, that you make a thermometer out of the Klein
bottle, if you don't know what to do with it.

TC