Mobius Bridges and Buildings - Numberphile

Key Takeaways

so idea of building a mobus bridge now one problem is that if you make a band and 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 a cross-section like a crescent and then you can move that cross-section you know through 180° and you still have a place to stand on for from one end to the other so basically you can kind of look down these Pathways and as you walk across and you're nice and on the 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 mobus band and the Hallmark of the mobus 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 and you could but you could still put this over a river like a bridge this as is you know would certainly function like a bridge right cool well it's just one of uh several possible designs wow here is a mobious band you can see it has this one twist and this is very simple it basically uh 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 um 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 and now you're walking on the silver surface here but now of course you have a tunnel so your structural support but that might be aesthetically more interesting or more pleasing so I think another totally practical way of building a mobus bridge I'm surprised people aren't building these they're brilliant maybe they do you know of anyone building these yet um there was one built uh not too long ago in Bristol and uh you have to look a little bit but I live in Bristol yeah better go and check it out I will yes so there supposedly have you I only have seen pictures of it so but it looks like it's an honest to God mov 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 mous 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 mobious twist essentially happens in that Loop over the the top you can see as the flat band that forms the rod bed goes up over the top it makes 18° 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 uh Bridge so it can actually hang the uh roadway you know from the uh vertical Arch that is oriented in the right way to give you maximal strength what about Mia's houses yes yeah they coming up so I claim both of these are mobious houses now what's happening with all the color let's look at this one first is it a mobious 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 mobious band does it make a practical house oh I think be oriented like that there are houses that are slanted like the towers in Madrid for instance right so there's nothing novel there you probably would have to either run the elevator at an angle which you can certainly do with 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 uh you know maybe uh 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 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 uh mobus band same idea we have very straight very conventional you know um building block you know with uh maybe three four stories uh worth of apartments or hotel rooms or whatever and then a much larger flat part along the bottom just as before that's where we might have you know the lobbies and the restaurants and the meeting rooms and the ballrooms and the library and stuff like that so again I think in both of these instances these are mobus buildings that really there's no doubt that they're mobus bands and they're very practical and from what I've seen by famous Architects kind of thinking about mob's houses it's it's much less obvious how they might function and uh um for me it was not always obvious to even see that there indeed are mobus configurations we got to get one of these things built you got to get a grant and get one made yep well somehow this doesn't want to come AP thing 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