Wednesday, December 26, 2012

Gift Scarf and Möbius

My sister, Ilene, gave to BBBH an "Infinity Scarf."  Trade-name, I guess.  Anyway, one glance at the beautifully-made fabric item assured me that it was a Möbius strip.  I announced this information to the gift recipient at once.  She was less than interested.

So I started with my standard seventh-grade presentation of the concept.  A  Möbius strip is a geometric figure which has only one side, and possesses but one edge.  (She:  So?)  Clearly this was going to rival in difficulty the actual presentation to a seventh grade class.

It is lots of fun to make a paper model of this figure with its weird properties, for with a pencil and a pair of scissors some amazing results can be obtained. (So?)

I am now talking to myself.  I did not even get to the rudimentary math involved, and that is the real fun!  The advantage lies with the seventh graders, for they are a captive audience, and may not wander from the precinct at will.


Never mind the background.

13 comments:

Lin said...

and then they all fell fast asleep.... ;)

Nobody fully appreciates the beauty of math...only the scarf, right?

Jim said...

I learned about Moebius and his strip in the 7th grade. I thought it was massively cool. A one-sided piece of paper! Wow! I still haven't figured out what it's good for, though.

Vee said...

Beautiful scarf - very chic! I agree with your BBBH that it need not be analyzed to be appreciated.

vanilla said...

Lin, no not all. Jim enjoyed it.

Jim, applications: continuous loop tape, double the playing time; conveyor belt, even wear on the entire surface, twice the life. Maybe other stuff, but I'm not an engineer.

I am pleased for your teacher that you stayed awake, in spite of Lin's comment.

Vee, well, yes. But there is beauty in mathematics too!

Secondary Roads said...

So get her a Klein bottle for her birthday and then try to explain the math for that. Multi-dimensional math can be a lot of fun.

vanilla said...

Chuck, I wasn't able to keep her attention long enough to explain this simple lesson. How would I deal with a Klein bottle? Might as well try to explain Schrodinger's cat.

Grace said...

I don't quite understand so I looked it up - understand a bit better (with a picture) - don't see the point except for making an interesting scarf - Since I have little or no depth perception and am spatially challenged this whole concept makes my head hurt. Nice scarf tho...,

vanilla said...

Grace, I am so sorry. I didn't mean to give you a headache. It is a lovely scarf, though, mathematics aside.

Secondary Roads said...

Your point is well taken.

Pearl said...

I have one of these, in a fluffy, warm blue.

Up in Mpls, just off the Mobius Strip,

Pearl

vanilla said...

Chuck, :-D

Pearl, take Klein's exit and hope I don't turn back on myself?

Sharkbytes said...

I would love to hear you expound on Mobius strips. Anyone who can present that to Jr Hi-ers and survive must have interesting things to say. They really are so strange, given how simply they can be made. They make me believe that almost anything is actually physically possible if we only understood how to do it.

vanilla said...

Shark, and speaking of possibilities, ideate this: bond two such strips along the respective edges and study the resulting Klein's bottle. Likely I could no longer "expound" but I did truly enjoy teaching junior high math!

Perhaps all things are possible.