Return Home

Krulwich Wonders: Mathematically-Challenging Bagels

Thursday, November 08, 2012 - 11:06 AM


Surgically, this will be complicated. Mathematically, it will be elegant. What we are going to do is take an ordinary bagel, and rather than cut it in half, we are going to turn it, delicately, into two intertwining, interlocked bagel parts, connected, unbroken, one twisting through one the other. In other words, a Mobius bagel.

George W. Hart

This is what mathematicians do on lazy afternoons. It's also a way to have more bagel surface to slap cream cheese on, says math teacher and sculptor George Hart, (who's so skinny, he couldn't do this often.)

Here's how it's done. If you had the hands of a surgeon and the brain of Pythagoras, you would take a knife and carve a gentle, 360 degree slice that dips down and comes back up in a perfect, interior swirl. This video demonstrates the ideal cut, but remember it's slicing an ideal bagel, with no crumbs, no imperfections, so this will never happen in real life.


But many in real life have tried. Since George Hart published his cutting scheme a few years ago, high schools now regularly ask students to make Mobius bagels (even if the term "Mobius" isn't quite right, because a true Mobius twists; these break).

Believe me, it isn't easy. I just tried, and the bagel fell apart because I couldn't get the knife to make the final near-to-the-surface pass without screwing up. But that's me. Some people have a gift.

Take "Kirill," a high school student who chose what appears to be a raisin bagel (which is crazy — adding random, lumpy obstacles is like throwing rocks onto a skating rink) and for his utensil, I think he used a cheap, plastic cafeteria knife, and yet, watch what he does.


One day, Kirill is going to be a brain surgeon.


Me? I'm in radio. My bagel's in tatters. I'm covered in crumbs. But I've got cream cheese, so I'll be fine. A little ashamed, a little chubbier, but fine.


More in:

Comments [6]

John from Indiana

The diagram shows that the cut through the side of the bagel rotates a full 360 degrees as you go around the bagel. This gives two interlocking rings when you try to take it apart, but neither is a Mobius band since the flat surface of either rotates 360 degrees as you go around it (ie, it has two half-twists, not one as in a standard Mobius band). But if you rotate the original cut only 180 degrees as you go around the bagel, you get a double length ring that doesn't separate into two parts (it's like two coils of a spring with the ends welded together), and it has two half-twists.

Take a Mobius band and cut it lengthwise (down the middle of the strip). Because of the half-twist in the original band, the two halves cross over and connect to each other, so you get a double-length band with three half-twists.

Try cutting the strip into thirds lengthwise. The outer two parts are like the two halves of the above example, so they from a double length band with three half-twists, while the middle part is just a thinner version of the original band. And these two parts are interlinked, but not as simply as in the bagel example.

Cut a Klein bottle into two symmetric halves, and you get two separate Mobius bands.

Dec. 14 2012 05:40 AM

Hart isn't that skinny, what a random thing to shove into the story.

Nov. 17 2012 08:06 PM
Laura Brown

Can't the publicity-seeking Ms Yang, her husband and their sockpuppets be banned from the comments now? This is beyond old.

Nov. 14 2012 04:14 PM

For those who have not forgotten the "Fact of the Matter" this again gets at the heart of the issue of Yellow Rain, and what was wrong with the podcast from a third party perspective.

Radiolab has so much to answer for.

Nov. 13 2012 07:31 PM
:D from the spot

I knew it, you are kinda cool :P
welcome back beb

Nov. 10 2012 04:59 PM

I'd rather eat a Krulwich.

Nov. 09 2012 01:04 PM

Leave a Comment

Email addresses are required but never displayed.

Supported by