# Ham sandwich theorem

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 580737.  Wed Jul 08, 2009 4:15 am In measure theory, the ham sandwich theorem states that any ham sandwich may be sliced exactly in half with only one cut. Well, alright, the theorem states that if you have n measurable objects in n-dimensional space, there exists at least one n-1-dimensional plane cutting all the objects in half. Taking n=3, and letting our objects be bread, ham, and bread, we get a ham sandwich cut in half. Mathematics is delicious.

 580769.  Wed Jul 08, 2009 6:11 am Does it work with jam (or spam)? What about things that don't rhyme with ham?

 580782.  Wed Jul 08, 2009 6:57 am Ham is about the only thing I'll eat in a sandwich - it can have lettuce etc in but I only really like ham in a sandwich. Gammon and SPAM are also acceptable :P as is BLT without the tomatoes (bleurgh).

 580793.  Wed Jul 08, 2009 7:12 am There is another theorem in mathematics called "sandwich theorem" – not ham sandwich or any other sandwich but just sandwich. This is a theorem in real analysis, which states (in as plain language as I can manage) that if you have a series lying between two other series, and the two outer series converge to the same limit, then the series in the middle also converges to the same limit. The middle series is, as it were, “sandwiched” between the other two. The theorem is also called the “squeeze theorem”. Yup, mathematics is delicious. On another delicious note, a topologist is described as a person who can’t tell the difference between a teacup and a doughnut. (More precisely he – or she – can’t tell the difference between a teacup with a handle and a torus-shaped American “donut”.)

 580802.  Wed Jul 08, 2009 7:40 am This kind of thread (because I can't understand a word of it) always impresses on me the inescapable truth that mathematicians can often be brilliant musicians, but most musicians (e.g. me) are absolutely crap mathematicians. I remember feeling utterly inadequate when I was at university and realizing that most of the top players in the University Orchestra were physicists and other number-crunching whizzos, not music undergraduates (e.g. me again) at all.

 580813.  Wed Jul 08, 2009 7:55 am It doesn't work with sausage sandwiches very well.

 581075.  Wed Jul 08, 2009 6:50 pm But I bet your subconscious is fantastic at math though Gaazy.

 581159.  Wed Jul 08, 2009 10:40 pm Crisp sandwiches tend to lose their filling when you cut them.

581178.  Thu Jul 09, 2009 1:53 am

 Davini994 wrote: But I bet your subconscious is fantastic at math though Gaazy.

You're very kind; but let me put it this way - I need pencil and paper to subtract 16 from 23.

Or, in that particular case, I could count it out on my fingers.

 581386.  Thu Jul 09, 2009 10:46 am You think you have 23 fingers Gaazy? It's worse than you think;) Personally, I suspect this ham sandwich theorem is just mathematicians trying to get one over on physicists, after we claimed the universe might be pringle shaped.

 581405.  Thu Jul 09, 2009 11:02 am I thought the universe was shaped like a 4 dimensional doughnut

 581553.  Thu Jul 09, 2009 2:31 pm 11, probably, at the last count.

 581567.  Thu Jul 09, 2009 3:05 pm To quote the doctorateless DJ Dr. Fox, "There's no actual evidence for it, but it is a scientific fact." By which I mean there's no real evidence for an 11-dimensional universe, but it does make for some pretty equations. A nice fact about a pringle or saddle shape is that it has negative curvature. Well, the middle bit of it does anyway. Oh, and don't worry about mathematicians being number-crunching whizzos. Most of us try to avoid using numbers as much as possible; anything over 2 is generally to be treated with some suspicion. Can't speak for the physicists though.

581643.  Thu Jul 09, 2009 4:51 pm

 ColinM wrote: A nice fact about a pringle or saddle shape is that it has negative curvature. Well, the middle bit of it does anyway.

With all of it being middle. I much prefer concepts and proofs to actually doing sums and calculations, but then I'm only slightly more physicist than mathematician really.

581651.  Thu Jul 09, 2009 5:04 pm

 ColinM wrote: A nice fact about a pringle or saddle shape is that it has negative curvature. Well, the middle bit of it does anyway.

Isn't it called a col?

Not sure where I dragged that up from.

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