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Ham sandwich theorem

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ColinM
580737.  Wed Jul 08, 2009 4:15 am Reply with quote

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.

 
themoog
580769.  Wed Jul 08, 2009 6:11 am Reply with quote

Does it work with jam (or spam)? What about things that don't rhyme with ham?

 
QiScorpion
580782.  Wed Jul 08, 2009 6:57 am Reply with quote

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).

 
Susannah Dingley
580793.  Wed Jul 08, 2009 7:12 am Reply with quote

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”.)

 
Gaazy
580802.  Wed Jul 08, 2009 7:40 am Reply with quote

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.

 
Ion Zone
580813.  Wed Jul 08, 2009 7:55 am Reply with quote

It doesn't work with sausage sandwiches very well.

 
Davini994
581075.  Wed Jul 08, 2009 6:50 pm Reply with quote

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

 
Sadurian Mike
581159.  Wed Jul 08, 2009 10:40 pm Reply with quote

Crisp sandwiches tend to lose their filling when you cut them.

 
Gaazy
581178.  Thu Jul 09, 2009 1:53 am Reply with quote

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.

There, I've admitted it.

 
Davini994
581386.  Thu Jul 09, 2009 10:46 am Reply with quote

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.

 
IronMonkey
581405.  Thu Jul 09, 2009 11:02 am Reply with quote

I thought the universe was shaped like a 4 dimensional doughnut

 
Janet H
581553.  Thu Jul 09, 2009 2:31 pm Reply with quote

11, probably, at the last count.

 
ColinM
581567.  Thu Jul 09, 2009 3:05 pm Reply with quote

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.

 
Davini994
581643.  Thu Jul 09, 2009 4:51 pm Reply with quote

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.

 
Posital
581651.  Thu Jul 09, 2009 5:04 pm Reply with quote

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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