Three Nested Klein Bottles

Nested Klein Bottles_Science Museum

This is one of a series of glass Klein bottles made by Alan Bennett in Bedford, United Kingdom for the Science Museum, London. It consists of three Klein bottles, one inside another. A Klein bottle is a surface which has no edges, no outside or inside and cannot properly be constructed in three dimensions. In the series Alan Bennett made Klein bottles analogous to Mobius strips with odd numbers of twists greater than one.

I disagree that it “cannot properly be constructed in three dimensions” as it obviously has been.  Perhaps they meant defined…

[Image and description from here, via somewhere else.]

[UPDATE: Here’s a visual summary of a single Klein Bottle, showing its relationship with a Mobius Strip (thanks to Strider).]

Author: Bunk Strutts

Boogah Boogah.

17 thoughts on “Three Nested Klein Bottles”

  1. Heh. Okay, Necro, you’ve redeemed yourself. =)

    Thelit– NOOO! No self respecting guy would waste a beer in such a contraption. I could see wasting a bottle of cheap wine in it, though, so that when the beers are gone there’s another puzzle to solve… with a hammer and a paper filter.

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  2. Tony– First, you melt some glass. Then you mess with it.
    The glass-blowing class I took in college was fun. It was in the middle of winter, and we got tans from standing in front of the gas-fired glory holes, messing with glowing molten glass. I loved it.

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  3. Hi Bunk. I think the person meant that, klein bottles are “hard to describe” in three dimensions, since the surface of the bottle is only one-sided (it opens into itself, so that the inside and the outside are ultimately the same side). Even stranger, the volume of this bottle is probably zero because the the issue of the one-sided surface.

    Another mad glassblower, doing klein beer mugs (or Klein Steins): http://www.kleinbottle.com/drinking_mug_klein_bottle.htm

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  4. strider–
    Klein Steins! Whatta concept! Great find, dudeness. Since the volume of a Klein Stein is zero, as it has no definable interior or exterior, any amount of liquid that it contains should have no volume either, and you, Necro and I could sit around a Klein Keg and tell stories all night while getting drunk on nothing. Serious money savings.

    What is fasckinating to me is that if you were to split a flexible Klein bottle, the result is a Mobius Strip, another related anomaly. [See the Update Linkoid above.]

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  5. Just an fyi, they mean what they said about properly constructed. A true Klein Bottle can not exist in the real world. It is a mathematical construction in R^4, or four dimensional space. What you see is a representation of a Klein bottle in three dimensions. See how the bottle intersects every time the stem turns inward? Well, a real Klein bottle doesn’t actually intersect in such a spot. A klein bottle never intersects itself, nor does it have definable edges. By intersecting, the three dimensional representations gain perspective, allowing them to have both a definable inside and outside, and volume. A klein bottle is kinda like a tesseract; we can pin it down mathematically, but no human can actually envision it since we are three dimensional creatures and they are four dimensional objects.
    And before anyone bothers bringing up the trivial argument- time is NOT the fourth dimension referred to. It is a fourth PHYSICAL dimension. NO, time is NOT a physical dimension. Don’t argue it, because you are wrong.

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  6. Someone– A Klein bottle is a topographical curiosity in 3D, has nothing to do with time, and nobody mentioned the 4th dimension. All I know is I was in love with Marilyn McCoo, but she was in the 5th Dimension.

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