Math theorem: the most misshapen ham sandwich can always be cut into two perfect halves


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You cut, I’ll choose. Fairer and easier :grin:


I love Numberphile. At the end they should have asked her to cut a ham and cheese sandwich, though. There’s another good one where Matt Parker shows that a 9 dimensional sphere is larger than the bounding box that defines it.

Ah, here:


Why doesn’t the ham sandwich theorem follow directly from the fact that any volume with measure has a centroid? Or does that not hold for n > 3?


Does the theorem also explain why anybody would demand mathematically-perfect sandwiches?


So the trick is, you take the sandwich bits, wad them up into a ball, turn the knife upside down, balance the sandwich wad on the knife edge, and push down; thus creating 2 perfect sandwich “halves”.

Math is not so hard when you apply some Physics.


Are there any other theorems that aren’t kosher or halal?


I’m glad I watched this. It will alleviate some of the pressure I feel when assembling ham sandwiches at the sandwich factory. If my boss criticizes me for making them sloppy I will be able to reassure him that it doesn’t matter.

Unless they include a cheese slice. Then we’ll need hyperdimensional sandwich slicer and those are expensive.


“Only works for a spheroid sandwich in a vacuum…”


Pfft. My knife has an edge sharper than the planck length, so I can cut the sandwich unequally by just wiggling the cloud of quantum blockchains.


You must be an only child. :laughing:.


Did your stock just go up 50%?


I figure adding the trifecta of cloud/quantum/blockchain to a knife sharpening joke should drive my “likes” up by at least 150%. Invest now for big gains!


I suppose some people have no standards…


One slice of bread, meat, fold. Half a sammich. No complications.


There is a meta-problem here. At what point does a sandwich cease to be a sandwich anymore, so that the act of cutting it in half becomes meaningless? If the two pieces of bread are so misaligned as to only have less than 50% overlapping and some portion of the meat itself is off the bread entirely, it’s no longer a sandwich. It’s like adding barbecue chicken to pizza. At that point, it’s no longer pizza.


Weird. Why do I suddenly have the urge to throw money at you?


There is no such thing as a misshapen sandwich, only shapen sandwiches…

And with that I think I’ll make an ugly sandwich right this moment.


They say it’s definitely possible to cut it into two perfect halves, but that the theorem doesn’t help them figure out how. That’s a theorem you can take to the bank, amirite?



Meh. Come back when they prove that the Banach-Tarski paradox applies to ham sandwiches, such that you can cut the sandwich into an infinite number of pieces, put them back together, and end up with two ham sandwiches that are identical to the original. That would be impressive, especially if each new sandwich had half the calories of the old one.