So idea of building a Möbius bridge; now
one problem is that if you make a band
you're supposed to walk on that band
across the bridge and that band slowly
turns, well, at the end of the bridge
you're falling into the water that's no
good right?
However, if you make your band kind of a
cross-section like a crescent and
then you can move that cross-section you know
through 180 degree and you still have a
place to stand on from one end to the
other. So basically you can kind of look
down this pathway and as you walk
across, on your nice and
horizontal surface, you simply find that
that crescent rotates around you. And
first you have your wall on the right
hand side and then you have it on your
left hand side but you can still walk
across straight. And then you simply
complete the loop over the top and make
sure that in doing so the whole thing
closes up on itself so it forms an
overall Möbius band and the hallmark of
the Möbius band is you start on this
side, and you walk around, and you walk
around on the inside, you walk around on
the inside, and you're suddenly on the
other side on that top loop. - (Brady: But you could still put this)
(over a river like a bridge?) - This as is
would certainly function like a bridge,
right? Well it's just one of several
possible designs. Here is a Möbius band,
you can see it has this one twist and
this is very simple; it basically- you're
walking on this pretty much flat surface
and then the twist
actually happens on the return path and
it essentially turns vertical and that
allows you to essentially support that
particular bridge. Or, if you don't want
to use as a structural support that
supports from below you could flip this
thing over and use it that way okay? Znd
now you're walking on the silver surface
here but now of course you have a tunnel
through your structural support but that
might be aesthetically more interesting
or more pleasing. So I think another
totally practical way of building a
Möbius bridge. - (I'm surprised people aren't)
(building these, they're brilliant! Maybe)
(they- do you know of anyone building)
(these yet?) - There was one built not too long
ago in Bristol and you have to look a
little bit but I- - (I live in Bristol!)
Better go and check it out! - (I will!)
So they're supposed to have- I've
only seen pictures of it so but it
looks like it's an honest-to-god Möbius
bridge even though it's kind of a
flamboyant return path that makes most
of the twisting and it's sort of a
horizontal loop like that. I think a more
elegant and really structural simple
Möbius bridge would be this one here;
again we can look and you can see where
you walk through or where you drive through, that is
very simple straight pathways. So all the
Möbius twists essentially happens in that
loop over the top. You can see, as the
flat bands that forms the rod bed goes
up over the top it makes a 180 degree
flip and comes back to the other side.
And that makes a perfect vertically
oriented arch that is strong enough so
it can act as a suspension bridge; so it
can actually hang the roadway, you know,
from the vertical arch that is oriented
in the right way to give you maximal strength.
What about Möbius houses? Yeah
they're coming up. So I claim both of
these are Möbius houses. Now what's
happening with all the colour? Let's look
at this one first.
Is it a Möbius band? Well we have to kind
of start up here, we're running down
there, we're running around the bottom,
we're coming up the other side - and yes
indeed we're on the other side so that
tells us this is indeed a Möbius band.
Does it make a practical house? Oh I
think if we orient it like that; there are
houses that are slanted like the towers in
Madrid for instance, right, so there's
nothing novel there. It probably would
have to either run the elevator at an
angle which you can certainly do as a
special track. So the question is, okay,
all the green stuff
may be windows, okay, and you have a lot of good
office space and you know maybe
apartments and the like that have, you
know, perfect views but then down here to
be consistent the green stuff is on top.
Well what does that mean? Well that's
where you put your lobby, that's where you
put your cafeteria, that's where you put your
library - and they all want skylights. On
the top of the flat part at the bottom
we essentially have a glass ceiling
and it nicely transitions into the
vertical part of the glass which gives
you the ordinary windows
that you might find in your office or in
your apartment. Here is another very
obvious Möbius band; same idea, we have
very straight very conventional you know
a building block you know with maybe
3-4 stories worth of apartments
or hotel rooms or whatever. And then a much
larger flat part along the bottom just
as before;
that's very might have the
lobbies and the restaurants and the
meeting rooms and ballrooms and library
and stuff like that. So again I think in
both of these instances these are Möbius
buildings that really- there's no doubt
that they're Möbius bands and they're
very practical. And from what I've seen
by famous architects kind of thinking
about Möbius houses it's it's much less
obvious how they might function and for
me it was not always obvious to even see
that there indeed are Möbius
configurations.
- (You've gotta get one of these things built, you've)
(got to get a grant and get one made.) - Yup.
Well, somehow this doesn't want to come apart here.
Okay if you look at that then it still hangs
together, it seems to be like one band -
actually it's a band that goes around
the loop twice and seems to be somewhat
intertwined.