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### Moebius Strip

Date: Mon, 14 Aug 95 09:57:45 EST
From: Anonymous
Subject: Moebius strip ??

Dr. Math, I know what a Mobius strip is, but I forget how to define its

Thanks!

Uri Portal
uri@sisoft.CL

Date: Tue, 15 Aug 1995 10:58:58 -0400 (EDT)
From: Dr. Ken
Subject: Re: Moebius strip ??

Hey there!

Well, I think you're probably referring to "nonorientability."  If a surface
is "orientable," that means you can define an "up" direction.  For instance,
if you're walking around on the surface of a sphere, you can define "up" as
the direction away from the center of the sphere.  If you walk around all
over the sphere pounding stakes into the ground telling people which way is
up, you'll never find yourself on the other side of the surface pounding
stakes into the reverse side of where you've pounded them before (which is
fortunate, since we live on the surface of a sphere).  On the other hand, a
Moebius strip is "nonorientable"; the opposite of orientable.  If you start
pounding in stakes on the surface of a Moebius strip and keep walking around
the strip, pretty soon you're going to end up on the reverse side, pounding
stakes into the "back" of the strip.  Simply put, the Moebius strip only has
one side.

Neat, huh?

-K

Date: Wed, 16 Aug 95
From: Anonymous
Subject: Moebius strip ??

What still confuses me, though, is that I could define a sphere in the
same way. If I pound a long enough stake intoany sphere (even the
good old Earth!) they will also go through and meet me on the other
side.

Uri Portal
uri@sisoft.CL

Date: Thu, 17 Aug 1995 14:55:40 -0400 (EDT)
From: Dr. Ken
Subject: Re: Moebius strip ??

Hello!

I think I've been a little unclear in my "pounding stakes" answer.  When I
say you should pound a stake into the ground, I just mean that you should
make sure people know which side of the surface is the "up" side.  So I
don't mean you should actually pound into the surface.  Perhaps a better
analogy would be to take toothpicks and scotch-tape them to the surface.
Just so someone who comes along after you knows which side is up.

Oh, I just had an idea.  An orientable surface is one where you can paint
one whole side of the surface red and the other side of the surface black.
On a sphere, you could paint the outside red and the inside black.  But on a
Moebius strip, you can't do that, because if you started coloring one side,
you'd soon find out that you'd colored the entire thing.

What I really recommend is to make one for yourself.  Have you tried?  If
you haven't and you'd like help, let us know.

- K

Date: Thu, 17 Aug 95 23:42:40 EST
From: Anonymous
Subject: Re: Moebius strip ??

Hello!!

First of all, I want to say that I appreciate your efforts to set me
straight in this matter. Unfortunately, I'm still confused in trying to
define which physical attribute differenciates a sphere from a Moebius
strip. You call the "other side" of a sphere its internal area. According
to this definition a Moebius strip also has an internal other side; just
hollow out its depth and paint it black.  (And I don't think that can say
that since a Moebius strip has only one surface, then its depth is
irrelevant since it is physically impossible to contruct a Moebius strip
without any depth.) And so even though I know what a Moebius strip looks
like, I'm still confused what made Moebius so happy when he discovered
it!

Thanks again,

Uri Portal
uri@sisoft.CL

Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

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