Bottle Design Brain Melter: The Handle is the Spout, the Opening is on the Bottom, the Inside and the Outside Are the Same Surface

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That there is the Klein Bottle, first conceived of in 1882 by German mathematician Felix Klein. Klein’s “non-orientable surface,” as it’s called in the math community, is like a Möbius strip in that you cannot distinguish inside from outside; follow it with your eyes and you’ll see one turns into the other, which makes me very, very uncomfortable.

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I’m told that the Klein Bottle is, in essence, two Möbius strips connected together. I’d like to start sketching that to work out how it goes together, but I can’t because I’m too stupid.

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