In the market for a Klein Bottle or just a wool hat shaped like one? Check out the selection at Acme Klein Bottle.
In 1882, Felix Klein imagined sewing two Möbius Loops together to create a single sided bottle with no boundary. Its inside is its outside. It contains itself.
Take a rectangle and join one pair of opposite sides — you’ll now have a cylinder. Now join the other pair of sides with a half-twist. That last step isn’t possible in our universe, sad to say. A true Klein Bottle requires 4-dimensions because the surface has to pass through itself without a hole.
It’s closed and non-orientable, so a symbol on its surface can be slid around on it and reappear backwards at the same place. You can’t do this trick on a sphere, doughnut, or pet ferret — they’re orientable.
My favorite is their $18,000 meter-tall Giant Klein Bottle… see the fascinating build photos on Acme’s site…
8 thoughts on “Klein Bottles ‘r’ them”
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Hey, that’s Cliff Stoll, of the “Cuckoo’s Egg” NOVA special and book from the 1990’s. Wondered what happened to that guy.
His FAQ says:
Are you the same guy that …
Yep, same guy.
BTW if you haven’t seen Stoll’s talk at TED.com, you really should watch it (includes a simple way to measure the speed of sound).
http://www.ted.com/talks/lang/eng/clifford_stoll_on_everything.html
Same guy who wrote “silicon snake oil”, this book where he says the internet is just a fad and e-commerce will never catch on. Oh, and people will never abandon print news for online news.
Who’s laughing now, Mr. Stoll? And ironically, who’s selling their stuff on the Internet now? Hmmm?