I did this small piece today :
(Sorry, the image was very small, so I enlarged it but it got blurred.)Well, when I say "I" did it, in fact it is copied from a drawing due to Thabit Ibn Qurra (826-901), I just decomposed it in a sequence of 5 figures. So the "today" is quite innacurate as well, and even more when you remark that it does provide a proof for Pythagore's Theorem, which is way older. (If you don't see why, call a,b and c the lengths of the sides of the triangles that appear in panels 2 and 3, c being the larger side, then in the first panel you have a black area of c square, and in the last one a black area of a square + b square.)
I don't think that this piece is very interesting as a comics (as a mathematical proof, it is brilliant - of course I take no pride in it since I just copied it and have nothing to do with its invention), but I publish it here because I think that there might be something to investigate here. There is a whole lot of "proofs without words" in mathematics. Wikipedia says that "The College Mathematics Journal runs a regular feature entitled `Proof without words' " (but I never looked at it), and there is a book of the same name containing hundreds of these proofs (I have looked at this book a while ago). So maybe one could take inspiration in these proofs to produce abstract comics that would be quite different from what I have seen until now (I guess), since its contents would be "concrete" representations of mathematical "abstract" concepts (I put both in quotes as I use these words in a quite unprecise way).
Of course, the interesting point would be not to just translate a mathematical graphic proof into a comics, but to introduce something new, which I did not make.
Well, I hope it does not sound too boring for people who do not like maths as I do. But for me this proof from Thabit Ibn Qurra is incredibly elegant, and deserved to be known, so even if my piece is not that interesting, I hope that those who didn't know it enjoyed it.
IaR.
this is lovely! good idea.
ReplyDeleteIt is really cool, and it makes sense... How shall I put it? The geometrical transformations required for the proof seem to me to be of a piece--or at least, on the same order of ideas--with those involved in sequencing many abstract comics. But why is panel 3 repeated?
ReplyDeleteHay, thanks Andrei, I had uploaded a wrong version, I have edited it now, there are only 4 panels and no repetition.
ReplyDeleteI was a bit tired yaesterday and did not notice the mistake.
Oh, I was imagining some abstruse mathematical reason for the repetition of the third panel. :)
ReplyDeleteNow it just looks like the entire construct just vanishes in the fifth panel--kind of a combination of Pythagoras and the 10 Oxherding Pictures in Zen? (But please don't fix it--I really like it like this.)
the shapes remind me slightly of Wlademir Dias Pino's visual poems A Ave (The Bird) & Solida (Solid), & Derek Beaulieu's Flatland. there's possibly even a connection with Shigeru Matsui's monotonous method-poems.
ReplyDeletea wordless proof by use of shapes is a fantastic idea.
I really like the idea of abstract comics illustrating mathematic principles. Thank you for sharing this.
ReplyDeleteLove it!
ReplyDeleteThis is brilliant. I am also interested in the use of abstract imagery to reproduce philosophical and mathematical ideas. Although, I hesitate to call it abstract at this point, if we are defining abtsraction as opposed to representation. Because this comic absolutely "represents ideas" through the manipulation of symbols (squares, triangles).
ReplyDeleteHowever, in terms of the philosophical meaning of the term abstraction, then this is entirely abstract (but most so-called "abstract" images become "particular" or "concrete" rather than abstract).
Very nice post anyhow. Great work!!!