Saturday 11 March 2017

The Bottle of Felix Klein

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The Klein bottle was first described in 1882 by the German mathematician Felix Klein.

Mathematically, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined. 

Felix Klein

Informally, it is a one-sided surface which, if travelled upon, could be followed back to the point of origin while flipping the traveller upside down.

It's a one-sided closed surface which cannot be embedded in three-dimensional Euclidean space, but it may be immersed as a cylinder looped back through itself to join with its other end from the "inside". It may be embedded in Euclidean space of dimensions 4 and higher.

The above text is from Wikipedia; similarly I can't better the following excellent videos, from Hannover Uni and the folk at, in conveying the essentials of The Klein Bottle. First though, here's an illustration of an unusual hex klein bottle that is 3D printable

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"Hodges emitted a scream the like of which
I hadn't heard since his scrotum was burned off
during my experiment with fluorine gas last year."

The Exotic Experimentation of Ernest Glitch,
Victorian Science with a Smile

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Search for Ernest Glitch on your Kindle
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Unrelated to this post, below is an example of
eclectic science esoterica 

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WARNING - Many subjects outlined within this site are extremely dangerous and are provided here for information only. Please don`t experiment with high voltages or chemicals unless you are fully conversant with safe laboratory practices. No liability will be accepted for death, injury or damage arising from experimentation using any information or materials supplied.