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How to Slice a Bagel into Two Linked Halves

Started by Elder Iptuous, December 08, 2009, 08:50:30 PM

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Elder Iptuous

Mathematically Correct Breakfast
How to Slice a Bagel into Two Linked Halves by George W. Hart



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.




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.


http://www.georgehart.com/bagel/bagel.html

Mesozoic Mister Nigel

"I'm guessing it was January 2007, a meeting in Bethesda, we got a bag of bees and just started smashing them on the desk," Charles Wick said. "It was very complicated."


Richter

Elegant trick! 
I plan to do this to every bagel I am allowed to lacerate.
Quote from: Eater of Clowns on May 22, 2015, 03:00:53 AM
Anyone ever think about how Richter inhabits the same reality as you and just scream and scream and scream, but in a good way?   :lulz:

Friendly Neighborhood Mentat

Iason Ouabache

Mobius Bagel looks delicious!  Small nitpick though:

QuoteThe 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.

ABCDA is a plane, not a line.
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Quote from: Iason Ouabache on December 08, 2009, 09:58:56 PM
Mobius Bagel looks delicious!  Small nitpick though:

QuoteThe 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.

ABCDA is a plane, not a line.

No.  It's a line.  It and the opposite (red) line mark the lines at which the outer surface of the bagel crosses the surface that will divide the bagels.  I don't know if it's appropriate to call the cut-surface a plane, but you sound like you'd know.