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
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.