
Proofs without words - J3L2404
http://mathoverflow.net/questions/8846/proofs-without-words
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robinhouston
That’s a wonderful compendium of graphical proofs. Math Overflow has become
such an important mathematical resource: you could imagine this thread being a
pretty good short book.

Graphical reasoning can be transformative, when it’s possible. In the field I
worked on as a PhD student, string diagrams are amazingly powerful
(<http://ncatlab.org/nlab/show/string+diagram>).

(I introduced the string diagram notation into my dissertation specifically
for the sake of one particular proof that would have been incomprehensible
expressed any other way.)

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jlaurend
The Art of Problem Solving has a page of cool little applets:
[http://www.artofproblemsolving.com/Resources/articles.php?pa...](http://www.artofproblemsolving.com/Resources/articles.php?page=gallery)

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blahedo
I _love_ visual proofs, but the problem with them is that they rarely work
without _some_ explanation (and the ones that seem to work without some
explanation are often those that re-express theorems you already sort of
understand). What the visual proof does is eliminate _excess_ words so that
you have multiple streams of information.

For instance, I have published a cool visual proof of the amortised analysis
of array resizing,[0] but even in animated form it would take at least a
_little_ bit of explanation for someone who didn't already know the basic
proof to understand what's going on with it. The elegance of it is that I only
need _a few_ words to explain what the visuals mean.

[0] The long abstract is at <http://www.blahedo.org/papers/dblaheta-
iticse09-amort.pdf> and the slides from my presentation---which from page 4 or
so serve as an animated proof-with-few words---is at
[http://www.blahedo.org/papers/dblaheta-iticse09-amort-
talk.p...](http://www.blahedo.org/papers/dblaheta-iticse09-amort-talk.pdf)

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juiceandjuice
This is cool, although I thought it was going to be something different.

One of my biggest pet peeves with ADHD trying to work on a Physics/Math degree
was the excessive wordiness of books. I generally have a photographic and
methodic memory, and so many proofs have tons and tons of words in them.

Oddly enough, I got along best with the older russian professors. I talked
with one of my professors about this. I guess most of them had been taught in
a much less wordy matter, and taught with even less words because English
wasn't their primary language.

There's a few books that have been around forever, and they have a completely
different level of readability between the editions. The Churchill/Brown book
of Complex Variables and Applications has added something like 100+ pages of
wordiness to the book since the 60's edition.

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gmartres
There's a great book with that exact title:
[http://books.google.com/books?id=cyyhZr-
SffcC&lpg=PP1...](http://books.google.com/books?id=cyyhZr-
SffcC&lpg=PP1&dq=%22proofs%20without%20words%22%20book&pg=PP1#v=onepage&q&f=false)
See also part 2(not available on google books apparently).

