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Old 07-24-2016, 02:28 AM
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Klein Bottle

This model is a 3 dimensional representation of a Klein bottle. It illustrates that a Klein bottle comprises 2 Mobius bands connected by a conventional 2 sided surface.
It is made with just 2 pieces of card.
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File Type: pdf Klein.pdf (69.1 KB, 37 views)
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Old 07-24-2016, 02:47 AM
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Very cool!
There are many people now who believe that the earth is flat. (crazy, right?)
I believe the earth is a Klein Bottle.
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Old 07-26-2016, 02:46 AM
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Voila!

If you cut the blue and red bits out you get 2 Mobius bands and a simple 2 sided strip.

And if you cut a band down the middle you get the band twice as long with a double twist.

I will have to put tabs on the mitres though!
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Old 07-26-2016, 06:36 AM
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It looks like the track plan of "A Subway Named Moebius."

Internet Book List :: Book Information: Subway Named Moebius, a

Don
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Old 07-26-2016, 08:44 AM
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That is a nice looking Klein bottle.
The Japanese Gallery on the Pepakura site has a Klein bottle in PDO format. ID:00029.
Japanese Pepakura Gallery ID: 00029
It is good to see the different ways that people represent the same idea.
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Old 08-10-2016, 04:15 AM
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A Klein what? Crikey, I had never heard of such a thing until now! For the others out there, like me, who are new to such things, have a look here:
https://en.m.wikipedia.org/wiki/Klein_bottle
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Old 08-11-2016, 01:22 AM
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Just for fun

Mobius Band
Cut a 50mm (2") strip from the long side of an A4 or letter size sheet of print paper.
Glue the ends together with a half twist.
Cut along its length down the middle and 1) What do you get?
Cut down the middle again and 2) What do you get?
And the last question, With the remainder of the sheet of paper, can you join the long edges together with a half twist?
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Old 08-11-2016, 11:50 AM
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Ah, the Klein Bottle. A completely misunderstood object.

Our eyeballs are klein bottles, as are the heads of our femur bones, to name just a few vital parts of our anatomy. The legs in my avatar are the two mobius strips that form, ....a klein bottle!
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Old 08-11-2016, 08:16 PM
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What a clever, and appreciated, contribution!
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Old 08-12-2016, 01:44 AM
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The Klein Bottle should actually be visualised as a 4 dimensional object. Hence there is no need for the base to penetrate the bottle wall in order to attach to the rim.
I am careful to describe my model as "A 3 dimensional representation of a Klein bottle".
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