Ok, so the mathematicians among you will point out that they're not quite Mobius bagels, but they are interesting from a geometry and topological viewpoint. And tasty.
We're going to make two inter-locking half bagels, which look quite impressive, just from a plain old normal bagel. They key is cutting it in the right manner.
I first found how to do this on George Hart's website: http://www.georgehart.com/bagel/bagel.html
But I haven't seen an instructable on this yet, so I thought I'd share it, and bring a bit more maths to the breakfast table.
We will need:
1 Knife, fairly narrow, serrated kind is best, but others will work
Step 1: The Cut, Pt1
The key to cutting it correctly is to be able to visualise rotating around the bagel. I find it easiest to make a couple of 'marker' incisions.
Looking at the bagel 'head on', at the 9 o'clock position, insert the knife into the bagel horizontally. Then at the 6 o clock position, cut into it from below (see photo). Then joint the two up in a diagonal cut so you are rotating the knife around 90degrees through the cut.
Step 2: The Cut Pt 2
Now repeat the process around to the 3 o clock position on the bagel. Again a horizontal incision beforehand might help give you somewhere to 'aim' for. Remember to keep rotating the knife around the bagel as you cut through. by the time you have finished this cut, you will start to be able to see the shape of the curved cut, which will utimately run round the entire bagel.
Step 3: The Cut Pts 3 and 4
Now continue the process around the bagel. By the time you have cut all the way around the bagel, the cut will have rotate 360 degrees in the plane of the bagel, but also 360 degrees in the plane of the cross section of the bagel.
Once the cut is complete, separate and add topping!
Step 4: Voila
It's a bit trickier to toast, but more aesthetically pleasing. And as George Hart points out, there's more room for your topping!