• "Spreading the ideas of freedom loving people on matters regarding metals, finance, politics, government and many other topics"

Klein bottle

BarnacleBob

Exoriare aliquis nostris ex ossibus ultor
Founding Member
GIM Hall Of Fame
Joined
Oct 15, 2012
Messages
19,078
Reaction score
43,137
images.jpeg



 

Winston_Room101

Silver Miner
Joined
Mar 31, 2010
Messages
522
Reaction score
348
Is Topology Not Fun ....

Place a finger on your nose ... and then
without lifting your finger from your skins' surface
move your finger to the inside of your mouth ... continue
moving your finger down your esophagus ( a thought experiment ) ...
thur your small intestine ...
thur your large intestine ... and out the other end
with your finger now returned to your skins' exterior surface

and so now it has been demonstrated that
the surface of your skin is the
same surface as the interior of your digestive system

FWIW
 

Fatrat

Site Supporter
Midas Member
Site Supporter
Joined
Apr 15, 2018
Messages
7,220
Reaction score
8,825
Neat.....
 

arminius

Argentate Bluster
Sr Midas Sup +++
Platinum Bling
Joined
Jun 6, 2011
Messages
7,212
Reaction score
11,793
Is Topology Not Fun ....

Place a finger on your nose ... and then
without lifting your finger from your skins' surface
move your finger to the inside of your mouth ... continue
moving your finger down your esophagus ( a thought experiment ) ...
thur your small intestine ...
thur your large intestine ... and out the other end
with your finger now returned to your skins' exterior surface

and so now it has been demonstrated that
the surface of your skin is the
same surface as the interior of your digestive system

FWIW

To do that, that finger needs to be at least 20+ feet long...
 

Bottom Feeder

Hypophthalmichthys molitrix
Midas Member
Midas Supporter ++
Joined
Mar 31, 2010
Messages
14,759
Reaction score
31,781
Location
SnowFlake City
another topology gotcha —
You cannot turn a torus inside out (think an inner-tube)
(without destroying it, that is)
 

Unca Walt

Midas Member
Midas Member
Site Supporter ++
Joined
Mar 15, 2011
Messages
15,425
Reaction score
31,083
Location
South Floriduh
And if you cut a Klein bottle in half the right way, you get two Mobius strips.

If you then cut the Mobius strip lengthwise all the way around...

You get a smaller Mobius strip. But you also get a 3-dimensional strip of twisted paper that is looped through the new Mobius strip.
 

Unca Walt

Midas Member
Midas Member
Site Supporter ++
Joined
Mar 15, 2011
Messages
15,425
Reaction score
31,083
Location
South Floriduh
One more -- I attended a topological luncheon one time where the napkin holders were Mobius strips, and the coffee was served in Klein bottles. Nothing sinister happened to the coffee.

You can picture how a Klein bottle can be a coffee cup if you hold it "upside down" (eg: skinny, bendy part down, and they had holders on the table to keep the Klein bottles upright.)
1634048060749.png


Nowadays, you can go to the Road Runner/Wiley Coyote store: Acme Klein bottle Mug. $93.

You can get a coffee mug Klein bottle -- the photo seems to make no sense, so I will add the diagram of what you are looking at:

1634047777498.png

1634047826673.png