Math Isn't Always The Answer

And this


is what?

It's from George W. Hart's "Mathematically Correct Breakfast: How to Slice a Bagel into Two Linked Halves"

It is not hard to cut a bagel into two equal halves which are linked like two links of a chain. To start, you must visualize four key points. Center the bagel at the origin, circling the Z axis. A is the highest point above the +X axis. B is where the +Y axis enters the bagel. C is the lowest point below the -X axis. D is where the -Y axis exits the bagel.

These sharpie markings on the bagel are just to help visualize the geometry
and the points. You don't need to actually write on the bagel to cut it properly.

The line ABCDA, which goes smoothly through all four key points, is the cut line.
As it goes 360 degrees around the Z axis, it also goes 360 degrees around the bagel.

The red line is like the black line but is rotated 180 degrees (around Z or through the hole). An ideal knife could enter on the black line and come out exactly opposite, on the red line. But in practice, it is easier to cut in halfway on both the black line and the red line. The cutting surface is a two-twist Mobius strip; it has two sides, one for each half.

After being cut, the two halves can be moved but are still linked together, each passing through the hole of the other. (So when you buy your bagels, pick ones with the biggest holes.) If you visualize the key points and a smooth curve connecting them, you do not need to draw on the bagel. Here the two parts are pulled slightly apart.

If your cut is neat, the two halves are congruent. They are of the same handedness.
(You can make both be the opposite handedness if you follow these instructions in a mirror.) You can toast them in a toaster oven while linked together, but move them around every minute or so, otherwise some parts will cook much more than others, as shown in this half.

But this is unintelligeable if you don;t see the illustrations.