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Klein Bottle Toilet Roll

... never runs out ....
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Inspired by ideas for re-using toilet roll cores.

A Klein Bottle has, theoretically, an infinite surface area, since it has only one surface and a single edge.

Therefore, a toilet roll wound on a Klein Bottle will have a similar infinte surface area.

Therefore it can never run out .....

Q.E.D.

8th of 7, Dec 13 2007

Tinkertoy bog roll Tinkertoy_20bog_20roll_20adapter
Prior art [8th of 7, Dec 13 2007]

(?) One Tube Deserves Another One_20Tube_20Deserves_20Another
Prior Art [8th of 7, Dec 13 2007]

[link]






       Oh dear oh dear. No. A Klein bottle has an unbounded surface, not an infinite one. In this sense it is no different to a sphere.   

       Also, I suspect that toilet paper wound on a Klein core would come off in the form a Möebius strip. Do you really want to wipe your bottom on something with only one surface?
MaxwellBuchanan, Dec 13 2007
  

       no-one likes a smart arse!   

       and the puppies do what?
po, Dec 13 2007
  

       Who's calling me smart???   

       It's true that puppies also have one useable surface. But they're much more absorbent and can be cleaned.
MaxwellBuchanan, Dec 13 2007
  

       // A Klein bottle has an unbounded surface, not an infinite one //   

       Yes, we know.... just testing.   

       We find the whole Möebius strip thing deeply disturbing.   

       // and the puppies do what? //   

       Disappear into hyperspace, possibly .....   

       W further propose a stylish tessseract-based holder for the core.   

       // Who's calling me smart??? //   

       A Tellytubby..... could be a complement, could be anything ....
8th of 7, Dec 13 2007
  

       I shall mull on this mootness.
MaxwellBuchanan, Dec 13 2007
  

       Now I may be wrong on this, but all of the Klein bottles I've seen only have a single concavity. This would make it impossible to use a standard pass-through mounting. You could mount it gravitationally (i.e., "set it") on a peg, but the concavity will need to be / not be filled with tissue paper as well. I think the only way out would be to have an electromagnetic support in that tesseract, and a ferrous core so that it can be magnetically suspended. However, this would naturally be almost entirely friction-free, so if you gave the endless roll a yank, and it never stops...
lurch, Dec 13 2007
  

       I shall have to mull on that one too.
MaxwellBuchanan, Dec 13 2007
  

       // Why not use donuts ? //   

       These too have one useable surface .... are you proposing also that they are "cleaned and used again" ?   

       If so, for what function ?   

       Are we talking chocolate-coated ring doughnuts here EEEEEWWWWWWww.....
8th of 7, Dec 14 2007
  

       //It's true that puppies also have one useable surface. But they're much more absorbent and can be cleaned//   

       Given cats' proclivity towards constant washing, might I suggest keeping one or two of those handy instead; by the time you need one it will have cleaned itself already, saving you the bother.   

       Re: the original suggestion: while useful to the extent that when you come to the end of a Moebian toilet roll you never have to remember if you've used the other side, that roll is of a finite length.
FlyingToaster, Dec 14 2007
  
      
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