I don't think this is completely true. There may not be tons of "proofs without words" in it, but the book Proofs from the Book is a great example of a nice collection of elegant proofs of elementary propositions that convince at a level that's much more effective than a pure, logical demonstration. Sure, you won't find these things in math journals -- you have to look in things like Mathematics Magazine, College Mathematics Journal, and various recreational mathematics and mathematics education journals. The fact that it's out there in print shows that somebody values this stuff.
I also didn't realize MathOverflow existed. On a whim, I typed in physicsoverflow.net, and it turns out that exists as well (though not well populated at all).
Sorry if we're still appearing hostile. We have a very focused target audience -- people doing mathematical research -- and in order to serve that community best we turn away questions at inappropriate levels (i.e. what should be 'standard material' of a mathematics undergraduate education at a good university). We try to do that politely, and offer suggestions of other places to try, but I know we don't always succeed.
Wow, the real number line to the open interval one is spectacular. I've always been interested in infinity and came up with some proofs of stuff like this during college, but this is such a nice proof.
I showed nearly that same picture to a class just two weeks ago. (I didn't draw the whole circle or the line segment representing the interval above it -- I just drew a line and a semicircle and said "this (pointing at the semicircle) is the unit interval bent into a semicircle.)" It's a very powerful demonstration, IMO.
Sure. The total number of yellow balls (the ones not in bottom row), is 1+2+3+...+(n-1). But each yellow ball determines exactly two blue balls (the ones in the bottom row): they're the ones you get by travelling left and right from the yellow ball in a straight line until the bottom. You can visually confirm it to be a 1-1 correspondence: different yellow balls will determine different pairs, and each pair is determined by some yellow ball. Therefore the total number of yellow balls is also the number of ways to choose 2 blue balls out of the total number of n blue balls.
aaah, any pair chooses a unique yellow ball - wow! thanks. if the image were animated, or showed a sequence of "selections" i think i would have gotten it.
Many of them don't seem to be complete proofs at all. It's not enough to draw pictures and claim that two areas are identical. You have to argue why the areas are identical.
I think you're missing the point. Its not that these are complete proofs or easy to understand proofs. The idea of a proof without words is that by staring at it and thinking about it, you can work out why the statement/theorem is true.
That being said, you're right that you need to be careful, as pointed out by Russel O'Conner's proof that 32.5 = 31.5 (with the colored triangles). However, someone who uses that as a "proof" is doing it wrong. When you find a proof without words, you need to actually write out the formulas that the picture indicates and make sure everything adds up (at least, for proofs of type you mentioned such as proving that areas are equal).
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[ 254 ms ] story [ 212 ms ] threadThings like this make me really appreciate the power of crowdsourcing. Hard to imagine how one could compile a list like this 25 years ago.
I wonder what other overflows exist.
I was thinking about creating a ProcrastinationOverflow but I haven't gotten around to it yet.
It's not meant for homework type questions, though, and they do shut those down right away.
I'm asking because I'm curious how approachable the concept/proof is.
I enjoy that by providing an example of a proof without words, it is proving (without words) that this is in fact possible.
http://www.catonmat.net/blog/visual-math-friday/
It is interesting that for proofs without words, comments are needed :)
That being said, you're right that you need to be careful, as pointed out by Russel O'Conner's proof that 32.5 = 31.5 (with the colored triangles). However, someone who uses that as a "proof" is doing it wrong. When you find a proof without words, you need to actually write out the formulas that the picture indicates and make sure everything adds up (at least, for proofs of type you mentioned such as proving that areas are equal).