Möbius Made Marvellously Easy

A Möbius band is a topological wonder: a two-dimensional entity happily residing in a three dimensional world.  It has only one edge and one flat side.

What is it about a Möbius scarf that makes it look so attractive?  It's the half-twist.  Without it, the plain loop looks like what it is: a simple short & wide cylinder hanging on a vertical cylinder (your neck).  But that half-twist is a trompe l'oeil effect that turns the flat cylinder into a graceful bias; or, at least, makes it look that way. It gives you the lovely, fabric-greedy, expensive bias drape appearance on straight-grain cheap.  Best of all, it can be dead easy to make. But, as I'll show below, if you try a slightly different approach, the results can be hilarious!

Start with a rectangle of fabric twice as high and as long as you'd like it to be (plus two seam allowances in each direction; wine is optional).  If you want to wear a single loop, 30" (75cm) will suffice; if you want to double or even triple it around your neck, increase the long dimension appropriately.

Fold this in half along the long axis with right sides together, and sew the long seam, leaving a gap large enough for your hand near one end.  I like to backstitch and clip off only one thread, leaving the other one long enough to sew up the gap once the scarf's finished.

Turn the scarf right side out, and fold it so that both raw edges are at left. Give it one twist as you do that - now the seam crosses under from the top to the bottom of the piece.

Lay the two ends one on the other and pin the right sides together; notice the seams are on opposite sides of the two openings.

Now reach into the little gap in the long seam and pull the pinned sections completely out through it. It's just like bagging the lining on a sleeve hem through a gap in the side seam of a jacket's lining.  Match up the rest of the two ends (they're one inside the other now - AHA!), and sew them completely together.  Once that's done, pull the scarf right side out again.

Now use that long thread and sew up the little gap. Your Möbius scarf is done!

Ready now for the "don't do this at home" trick?  You might wish to be "clever" (ahem) and simplify matters. You might want to sew the short edges together from the wrong side - thinking that it's easier to do that, and just turn the completed loop inside out once finished.  Heck, why on earth not?!

So you do your half twist, place and then pin the raw ends right sides together....

Sew up that short edge, and - you might think - you're all done, except for turning the lovely little scarf right side out.   Right......? 

Right!!! But your results aren't quite what you expected, are they?  Instead of a low but wide loop, you made a tall and skinny one.  Surprised?!  I sure was. 

Perfect if you happen to be one of the lovely Karen ladies, who are famous for having the longest necks in the world. 

That's topology for you, kids!  Live and learn.