Mathematically Correct Breakfast

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.)

Previously, previously.