Klein Bottle

By Edward W. Brown; posted January 12, 2011

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What is a Klein bottle.... It is a glass container of which the inside is also the outside, maybe a three-dimensional Möbius Strip ? A one-sided solid, perhaps.... Or a hyperdimensional venusian fly trap.

This example, at approximately one meter tall, is much larger than the usual labware curiosity.

The intricacies of producing this are described here: Under the direction of Bob Maiden, Killdee Scientific Glass has built this giant Klein Bottle from Pyrex and Duran Borosilicate tubing. Much of the work involved building specialized torches and shaping jig. Because of its size, Bob and his assistants had to carefully coordinate their hand motions and machine operations in a high temperature dance of glass.

To make the top tube, we used 24 special oxy-acetylene torches to heat 90 mm Pyrex tubing red hot. We then bent a near-hairpin curve in the glass pipe. The main, pear-shaped flask is blown from a 72 litre Pyrex blank, using a special, wide-swing glass lathe. The curved pieces must be welded to a precision of a millimeter -- all the while wearing flameproof aluminum pyrosuits. After assembling, welding, and firepolishing, the Klein Bottle gets annealed at 1200 degrees F, to relieve internal stress.

Mathematically, this is identical to our smaller Klein Bottles -- that is, topology does not care about changes in size. It's bigger than your average boundless thing.

This is a Giant Klein Bottle, resulting in a delightful German oxymoron, RiesenKLEINflasche (Many thanks to Georg Moritz of Stuttgart-Korntal for helping make such a flavorful play on words!)

To a mathematician, it's a one-sided bottle, homeomorphic to a disc with two crosscaps. To a glass worker, it's a major challenge in glassblowing. To the casual viewer, it's an accomplishment in art, glass, and mathematics.

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