Comments on Travels in a Mathematical World Blog: Pictorial proofs

Since I was the one suggesting the proof without w...

2011-12-22T19:11:09.544Z

Since I was the one suggesting the proof without words for this week's mathblogging.org picks, let me add that I do think the proof is elegant: it reduces the problem from the plane to the line, which is a typical mathematical strategy but nevertheless a deep one (just like going the other way around).

I also love the one Peter Rowlett posted -- it is one of my favorites because it is not a proof, it is much better than a proof! Like shining beacon it visualizes the problem at once, breaks Zeno's paradox and gives you a perfect picture to hold on to while you formalize a proof.

Here's a nice list http://mathoverflow.net/questions/8846/proofs-without-words (shameless plug 1: got it from mathblogging.org via our custom search "proof by picture" -- there's more).

Finally, (shameless plug 2) if you don't mind German, http://vimeo.com/10014698 (I was somewhat involved in this).

In fact, pictorial proofs are everywhere. Here'...

2011-12-21T22:24:39.750Z

In fact, pictorial proofs are everywhere. Here's one that's a bit more Marcel Marceau (it's kinetic! it tells a story!) - http://gaussianos.com/demostracion-sin-palabras-de-la-formula-para-calcular-el-area-de-un-circulo/

Mathblogging.org picked this "proof with no words" of a theorem by Gomory: http://mathhmagic.blogspot.com/2011/12/gomory.html

For me, it's very definitely in "cheeky five-year-old" territory - you only really see the cleverness of the proof once it's been explained in words. Otherwise, you might as well have come up with the proof independently.

I suppose it's a very good example because unless you send it through Google Translate it's unlikely you're able to read the Greek explanation!

On Twitter last night (Maths Jam night) I got repl...

2011-12-21T10:37:33.018Z

On Twitter last night (Maths Jam night) I got replies from @christianp: "I have yet to see a pictorial proof that was more Marcel Marceau than cheeky five-year-old keeping mute" and the Newcastle @MathsJam: "Young diagrams explain integer partitions very well".