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Mathematically Correct Breakfast - How to Slice a Bagel into Two Linked Halves. If a torus is cut by a Möbius strip it will split up into to interlocking rings.

It is not hard to cut a bagel into two equal halves which are linked like two links of a chain. Figure 1:

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.

It is much more fun to put cream cheese on these bagels than on an ordinary bagel. In additional to the intellectual stimulation, you get more cream cheese, because there is slightly more surface area. Topology problem: Modify the cut so the cutting surface is a one-twist Mobius strip. (You can still get cream cheese into the cut, but it doesn’t separate into two parts). See more at: Mathematically Correct Breakfast: How to Slice a Bagel into Two Linked Halves by George W. Hart.

Videos:  Cutting A Bagel & Interlocking Bagel Rings & Mathematically correct breakfast.

Images: How to Slice a Bagel into Two Linked Halves by George W. Hart - Cutting bagels into linked halves on Mathematica. - Interlocking Bagel Rings

I don’t but this is totally a thing, and you do it via my favorite method of identifying things ever; you set them on fire.

...no really. Pull a couple threads off of the edge, pull out your lighter (and one should always have a lighter on hand, even if one does not smoke, for on the fly campfire construction, Molotov cocktail lighting, minor acts of arson, and identifying mysterious fabrics).

If the fabric shrinks from the flame, then lights and beads up and melts, leaving little hard beads of plastic when you blow it out, and stinks of, well, burning plastic? It’s synthetic, or heavy on the synthetics in the blend.

If it does not shrink from the heat, lights, flares up, burns, smells of burning paper, and continues to glow for a second or three after being blown out? It’s cotton.

Rayon reacts much like cotton, but may glow for longer when blown out.

If it lights without shrinking, burns steadily with a bright flame, and smells of burning paper, it’s probably hemp or nettle or ramie (a relative of nettle native to southeast Asia that’s been called ‘Chinese linen’ for it’s use as a fiber plant going back thousands of years.)

If it acts like the above but takes a moment to catch, it’s linen.

If it burns slowly and curls (not shrinks) away from the flame, smells like burning hair, and leaves a bead that is easily crushed between your fingers into a black, gritty ash, it’s silk. Silk will also self-extinguish after a few moments.

Melted synthetic burns...if you ever want nightmares, go google them. Where I work, all fabrics have to be certified flame resistant, because everything around here is flammable as hell. They make us sit through several training films talking about the burns caused by synthetic fibers melting into (yes, folks, into) the skin because of industrial accidents.

They ain’t pretty.

Suffice to say, I only wear wool hats and gloves in the winter at work for damn good reason.

random

Straightforward. Soft and heavy, like morning before the coffee’s started brewing. Like that’s all there is to say.

Through laughter, over a chorus of voices, knowing it’ll strike home anyway. It’s meant for everyone here, after all.

Slipped under your tongue, twisted into something else. “I trust you,” maybe. Trust them to figure it out.

Instead of “thank you” or “see you soon” or “drive safe.” Because no matter what you say it’ll mean the same thing.

Casually, as if you don’t mean it. Trying like hell not to mean it.

Wrapped up in a question. How’s your day been, have you eaten, you know you can tell me anything, right? You know you can tell them anything. Right?

Under your breath while the whole house sleeps, just before you have to leave for the day. More for yourself than for them.

With a hand on their shoulder, a song on your lips, or a carton of their favorite ice cream in the freezer.

Over a nervous smile, biting back the just-this-side-of-desperate hope they’ll say it back.