One of my favourite images of all time. Stanley Kubrick. Ringling Brothers Circus. 1947.
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.
Maybe, that’s one of the reasons why I love bagel :)
I must try this.
I suspect it will lead to:
• lots of pieces of bagel
• no interlinked bagel rings
I stared at this for a few seconds but once I got it, I chuckled.
Don’t take puns for granite.
These jokes just keep getting boulder.
i don’t know, they’re kind of a lode of schist.
Now, now, there’s no need to get all butte hurt, lets just take a steppe back
Yeah, everyone, be gneiss.
I’m cracking up at this.
Thank you for that earth-shaking contribution.
Don’t mine me, I’m just marbling at the humor.
No reason to mica fuss about any of this
Pierre et Marie Curie dans leur laboratoire , vers 1898 .
Oh what a wonderful dream to wake up from. Now I'll give you five story ideas.
You're tired? Well I'm sorry but I must keep these ideas coming until it's almost 4am and you're dozing off on your computer/notebook.
I know how you can solve this plot hole.... with this scene.
That person over there looks like OC... oh! This gives me an idea! Who cares if you have nothing to write it down with.
Wow... here's a great way to word that scene you can't get down. Too bad in five minutes you won't remember much more than two sentences. From different paragraphs.
You know what would be great? Instead of this happening, this happens and I am so glad this brilliant idea makes you want to write and not focus on this geometry question!
Yeah, I got nothing.