How to Slice a Bagel into Two Linked Halves (2009)(georgehart.com)
georgehart.com
How to Slice a Bagel into Two Linked Halves (2009)
http://www.georgehart.com/bagel/bagel.html
22 comments
Here's a short series on math-based Thanksgiving foods. https://www.youtube.com/watch?v=F5RyVWI4Onk&list=PLaNzoFtkQ7... It's hard to know where to stop recommending Vi Hart projects, I find them consistently cool and fascinating, so I'll just mention her blog http://vihart.com/ and Patreon https://www.patreon.com/vihart
ah, I never put it together that they were related! That would be a fun family.
The manner of delivery is reminiscent of Steve “Protopod” Sutton’s [0] famous iced tea video. [1]
[0] https://www.youtube.com/user/protopod
[1] https://www.youtube.com/watch?v=hSkT77010fE
[0] https://www.youtube.com/user/protopod
[1] https://www.youtube.com/watch?v=hSkT77010fE
Hexaflexagons are great and Vi Hart is great. Nice share.
I prefer his other daughter, Vim Hart.
It turns out there's a sequel! http://www.georgehart.com/bagel/knot.html
"Waiter, my bagel has black magic marker all over it. I think I'll just have the omelette instead."
Exercise to the reader: How do you slice the bagel so that you can spread cream cheese continuously along both sides. In other words, can you make a Möbious bagel?
Make a cut through it shaped like a mobius strip - that is, a single 180 degree rotation instead of going the whole 360 degrees shown here.
To think about it another way, imagine if you took a mobius strip and constructed a semicircular lump of bread on the surface, extending it around until it connects back to itself. You've made a bagel!
Now take the mobius strip out of the middle, and the gap it leaves is the cut you're asking to make.
To think about it another way, imagine if you took a mobius strip and constructed a semicircular lump of bread on the surface, extending it around until it connects back to itself. You've made a bagel!
Now take the mobius strip out of the middle, and the gap it leaves is the cut you're asking to make.
Sounds like a job for some parchment and my weekend.
I wonder if I could sell bagel-sized silicone mobius strips for baking.
I wonder if I could sell bagel-sized silicone mobius strips for baking.
Potentially interesting to anyone with an oven, if you can capture 1% of that market you'll be rich!
I'd suggest raising a few million in seed funding and renting an office in downtown SF. If it doesn't pan out you can pivot into math-related silicone ice cube trays.
I'd suggest raising a few million in seed funding and renting an office in downtown SF. If it doesn't pan out you can pivot into math-related silicone ice cube trays.
The ICO is Monday. First 10,000 have an ERC20 address printed on the mold.
Yeah, I think you can just make a half-twist instead of a full twist like the article does. Or any number of full turns + 1/2.
Haven't attempted or vetted yet, but perhaps this? https://m.youtube.com/watch?v=NRvK_07KRV8
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I definitely saw a Mobious bagel on Youtube, perhaps about 5 years ago - my attempt to copy it failed, my bagel was too soft.
I should document this and make it my first HN post.
Don't you have a job?
This is the best article ever posted to Hacker News.
Sharing stories like these with the world is what the world wide web was made for.
My team at work thinks of every excuse possible to get bagels. Recently for a birthday, a work anniversary, and being restacked into new cubes. But this is the best possible excuse for bringing in bagels again on Monday.
Don't share it. Just wait until the next batch comes in and then cut a few like this while no one is watching.
The resulting workers comp report when someone slices their hand is going to be really interesting.
Of course if we could make a bagel cutter in the spirit of the popular bagel guillotine slicer that cuts a linked bagel we could be millonaires.
I didn’t know what I was getting into with that click, but now I’ve added bagels to our grocery list so I can do this.
Bagel, lox, cucumber and cream cheese has become my new favorite thing lately (bonus points for a squeeze of lemon, capers or some red onion if those things are to be found).
However, I of course have no bagels or bagel accessories on the one day I read about mathematically correct bagels :(
So yeah, added to my grocery list too!
However, I of course have no bagels or bagel accessories on the one day I read about mathematically correct bagels :(
So yeah, added to my grocery list too!
That was my dinner of choice throughout childhood. Love it still.
Numberphile video on this topic, including 3d-printed examples of some higher-order slicings: https://www.youtube.com/watch?v=3_VydFQmtZ8
I wonder if it's possible to repeat the process in such a way that you make a chain. I'm trying to visualize how but I'm not certain whether it could only make more links all attached in the same place.
I believe every link would be linked to every other link.
Not necessarily. Just as you could take a chain and stack the links such that the holes lined up, with enough precision, and a strong enough baked good, you could cut the bagel such that there were a chain of linked rings.
Well, if you cut the bagel according to this particular linked torodial method, to produce two links, you’d then be able to perform the traditional bagel slice on one of the linked halves, and that would produce a chain with three links...
But deriving from a single original torus, a chain with an arbitrary or infinite number of links, whereby each individual link is bound to no more than two other links? I’ll have to think about that one...
But deriving from a single original torus, a chain with an arbitrary or infinite number of links, whereby each individual link is bound to no more than two other links? I’ll have to think about that one...
you'd need a very thick bagel
Just had a brief discussion at work about bagels that started with a complaint about how they're never sliced all the way through.
After a couple minutes of back and forth an epiphany was realized that if they were pre-cut all the way through they'd get jumbled up and then we'd spend way too much time rifling through halves to find a matching one.
After a couple minutes of back and forth an epiphany was realized that if they were pre-cut all the way through they'd get jumbled up and then we'd spend way too much time rifling through halves to find a matching one.
Clearly, a candidate for inclusion in one of the fine academic journals on mathematics. Or the Martha Bakes cookbook.
Either way, bravo!
Either way, bravo!
I never knew I needed this information. I’m gonna go buy some bagels now.
Video of the process: https://www.youtube.com/watch?v=2T5FrZl04JY
Villarceau circles!
https://en.wikipedia.org/wiki/Villarceau_circles
https://en.wikipedia.org/wiki/Villarceau_circles
Is it a sin to put pineapple on it?
Someone please ask Professor Shewchuk (UC Berkeley) and Professor Demaine (MIT) to look at this! Perfect geometric problem for both of them.
Someone please ask Professor Shewchuk (UC Berkeley) and Professor Demaine (MIT) to look at this! Perfect geometric problem for both of them.
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I've tried never been able to achieve this with my hands and knives.
Now do it with a mug.
All the pictures in that link already show a mug.
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A mug is topologically equivalent to a bagel or donut or torus.
T-topologically w-what??
I mean yeah, that was the point of my remark.
To write something on topic as well:
There was a fun little challenge on puzzles.stackexchange I think, which relied on the same construction as this article. I couldn’t find it, but it went like this:
“You’re stuck on top of a tall building with nothing but a saw. There’s a ladder fastened to the side of the building, but it’s unfortunately not long enough to reach the ground; in fact it goes about half the height of the building from the top. Challenge is to get on the ground “safely”. You can cut into the ladder with your saw in any way you like and you can assume that the resulting pieces will be rigid, but won’t break under load.”
I mean yeah, that was the point of my remark.
To write something on topic as well:
There was a fun little challenge on puzzles.stackexchange I think, which relied on the same construction as this article. I couldn’t find it, but it went like this:
“You’re stuck on top of a tall building with nothing but a saw. There’s a ladder fastened to the side of the building, but it’s unfortunately not long enough to reach the ground; in fact it goes about half the height of the building from the top. Challenge is to get on the ground “safely”. You can cut into the ladder with your saw in any way you like and you can assume that the resulting pieces will be rigid, but won’t break under load.”
As far as I can tell this challenge would not require a twisted cut.
Please elaborate!
I think it would be possible to slice the ladder exactly in half, down its length, right?
Each rung would go from a cylinder to a half-cylinder, but should still be rigidly connected to either side of the ladder all the same.
Each rung would go from a cylinder to a half-cylinder, but should still be rigidly connected to either side of the ladder all the same.
The problem is then you have two short ladders. You throw your two half ladders off the roof and they don't magically stand end-to-end for you. You have to cut with a twist to ensure the last rungs are entangled with each other so the half-ladders are hooked together. Then you can hang one off the other and reach the ground.
See I was envisioning one of these: http://www.bates.co.za/BMS_Product_Images/ROUND%20TUBE%20LAD...
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I'd rather just have a mimosa. :/
Video tutorial please.
There's an addendum at the bottom of the page linking to a how-to video: http://www.youtube.com/watch?v=dN8AwGUaqDA
That family must have the best picnics!