Naked Science Forum

General Science => General Science => Topic started by: Geezer on 14/02/2011 07:50:48

Title: Where does Mobius end?
Post by: Geezer on 14/02/2011 07:50:48

If I can make a Mobius strip, can I also make a Mobius thingy with triangular cross section?

And, if I can make a Mobius thingy with triangular cross section, can I also make one (or two, or three) with rectangular cross section?

And if I can make..........

Where does it all end????

Title: Where does Mobius end?
Post by: graham.d on 14/02/2011 13:03:17

I should go and have another drink from your Klein bottle if I were you.

Title: Where does Mobius end?
Post by: imatfaal on 14/02/2011 16:42:27

Quote from: Geezer on 14/02/2011 07:50:48

If I can make a Mobius strip, can I also make a Mobius thingy with triangular cross section?

nope - if you imagine taking a mobius strip and adding two faces to convert a strip to a small section of triangular prism; at this point it seems fine, but of course as you carry on round the strip you go round twice and make a nice quadrilateral cross-section mobius.  Alternatively you can imagine taking a nice triangle cross sectional material that is flexible, loop it over and then twist one end by 180deg, they no longer match. 

Now if you had twisted by 120 degrees - and your triangle was equilateral, that's another question.  you can find a lovely example at fermilab http://www.maa.org/mathland/mathtrek_9_4_00.html. of course the rectangular cross section is easy - just use thicker and thicker paper.  I see no reason that you couldn't use any cross section with rotational symetry and twist by the angle of that symmetry

Title: Where does Mobius end?
Post by: Geezer on 14/02/2011 19:23:00

Yes, yes! Thanks!

The 120 degree twist thingy was what I had in mind. See, I was thinking that if fan belts were made that way, they would wear on all three sides (well, of course there really only is one side, but I think you know what I mean) and last 50% longer. Of course, a square section version would then last 100% longer. If we keep going with this, we'll eventually get to a round cross-section which, if my theory holds, will last indefinitely!

Title: Where does Mobius end?
Post by: Don_1 on 21/02/2011 16:29:49

Mobius? Is that the Latin version of Mobius Dickius by Hermanii Melvillius?

Title: Where does Mobius end?
Post by: imatfaal on 21/02/2011 16:45:15

And cue Life of Brian jokes in 3, 2, 1...

Title: Where does Mobius end?
Post by: Geezer on 21/02/2011 23:31:19

In the immortal words of Tom Jones,

"Pwease wewease me, wet me go...

Title: Where does Mobius end?
Post by: yor_on on 23/02/2011 10:05:26

How about a moebius sphere?

I'll take two,  thank you :)

Title: Where does Mobius end?
Post by: imatfaal on 23/02/2011 11:56:02

I think that would be cognate to the klein bottle

Title: Where does Mobius end?
Post by: Bill S on 05/03/2011 16:57:53

How about Mobius Stripus; an early strip joint on the Via Contorta, owned by Mafiosus Originalis?

Title: Where does Mobius end?
Post by: imatfaal on 07/03/2011 13:28:31

The perfect/worst (delete as applicable) strip joint - you don't have to cross the busy road to get to it, just stay on your side of road walk around the block and there it is right next to you.