How to make a Möbius bagel: Sliced just right the breakfast snack makes linked halves with curious mathematical properties
A mathematically inspired sculptor has demonstrated how to slice a single bagel into two interlocking halves with one long slice.
George Hart, who holds a PhD from MIT, explains how by making a sweeping cut around the bagel, with the cutting surface following a two-twist Möbius strip you get 'two equal halves which are linked like two links of a chain'.
But Dr Hart explains that the best part of the trick comes when you slather the two bagel halves with cream cheese. 'In additional to the intellectual stimulation, you get more cream cheese, because there is slightly more surface area,' he said.
The Mobius bagel: By making a sweeping cut around the bagel, with the cutting surface following a two-twist Möbius strip, you get two interlocking halves as in this picture
The MIT-trained mathematician provides step-by-step on how to do the culinary trick on his blog.
To begin with, he explains, you must visualise four key points around the bagel, with its central hole circling the Z axis.
A is the highest point above the +X axis; B is the point where the +Y axis enters the the doughy foodstuff; C is the lowest point below the -X axis; and D is where the -Y axis exits the bagel.
An imaginary line ABCDA running smoothly through the four key points is the line where you make your cut.
MIT-trained mathematician George Hart explained how to make the bagel on his blog: To begin with you must visualise four imaginary points on your bagel, which Dr Hart has drawn on here with a marker pen
The line of the cut: The cut is made through a line that connects all the points in one elegant 360-degree loop. It's easier, Dr Hart says, to draw another line on the opposite side and cut halfway through both
Like magic! After the bagel is cut, each half can be moved independently of the other; but they remain connected like the links of a chain, with each passing through the hole of the other
THE REMARKABLE MÖBIUS STRIP
The Möbius strip is a surface with only one side and only one boundary component discovered independently in 1858 by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing.
A model can easily be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop.
Möbius strips have found a number of surprising applications that exploit a remarkable property they possess: one-sidedness. As a result of the half twist, the Möbius Strip has only one side and one edge.
Giant Möbius Strips have been used as conveyor belts (to make them last longer, since 'each side' gets the same amount of wear) and as continuous-loop recording tapes (to double the playing time).
To carve the bagel more easily, Dr Hart recommends visualising a second line on exactly the opposite side to the bagel, then cutting halfway through both.
'The cutting surface is a two-twist Möbius strip,' explains Dr Hart. 'It has two sides, one for each half.'
After the bagel is cut, each half can be moved independently of the other; but they remain connected like the links of a chain, with each passing through the hole of the other.
Now for the fun part - eating the bagel.
'You can toast them in a toaster oven while linked together,' said Dr Hart.
'But move them around every minute or so, otherwise some parts will cook much more than others.
'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.'
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