Suggestions for topics in a public talk about art and mathematics
The influence of the 4th dimension on art. Duchamp is an obvious example. Art historian Linda Henderson believes that Picasso was 4-dimensionally influenced as does Tony Robbin who clearly and unabashedly is. Tony's work influenced me to draw a bunch of stuff at my website, and these drawings are directly influencing some of the mathematics that I am doing. In addition, you might want to mention Carlos Seguin (sic?) and of course, George Hart. His daughter Vi Hart has been in the news recently.
The problem is not that there is a lack of material, but there is too much. Many great and serious artists are influenced by us, and as I indicated above some of us are influenced by them. You should also look at the work of Radmila Sazdonovic and Slavan Jablan for example.
I also can't resist mentioning Kaplan and Bosch's work using the traveling salesman problem to reproduce famous artworks; i.e., TSP art. See these links:
For example, this reproduction of the Mona Lisa is actually a solution to a traveling salesman problem. There's a single path that creates the image.
You might get some inspiration from the articles in the Journal of Mathematics and the Arts (published by Taylor and Francis - http://www.informaworld.com/smpp/title~content=t755420531~db=all) and/or from the proceedings of the Bridges Conferences (which deal with connections between mathematics and the arts) - http://www.bridgesmathart.org/
There is a lot of beautiful mathematics (mostly, if not all geometry) in perspective drawing. I've heard Annalisa Crannell give beautiful lectures on this. Unfortunately, her book isn't due out until July 2011 (you can find it on amazon, and I can only include one link). There is a nice description of a public lecture she gave at the MAA, with audio of the lecture and a few embedded videos:
I heard Thomas Banchoff give a nice talk about Salvador Dali's work a few years ago. Apparently they were even friends.
Here's a link to a lecture by Banchoff on Dali.
It looks like Banchoff wrote a paper in
Spanish Catalan on Dali, too:
"La Quarta Dimensio i Salvador Dali," Breu Viatge al mon de la Mathematica, 1 (1984), pp. 19-24.
Even with my
poor Spanish nonexistent Catalan skills I can translate the title as "The Fourth Dimension and (or "in"?) Salvador Dali." :)
Related videos on Youtube
Cheerful Parsnip almost 2 years
I've been giving a public talk about Art and Mathematics for a few years now as part of my University's outreach program. Audience members are usually well-educated but may not have much knowledge of math. I've been concentrating on explaining Richard Taylor's analysis of Jackson Pollock's work using fractal dimension, but I'm looking to revise the talk, and wonder if anyone has some good ideas about what might go in it. M.C. Escher and Helaman Ferguson's work are some obvious possibilities, but I'd like to hear other ideas.
Edit: I'd like to thank the community for their suggestions, and report back that Kaplan and Bosch's TSP art was a real crowd pleaser. The audience was fascinated by the idea that the Mona Lisa picture was traced out by a single intricate line. I also mentioned Tony Robbin and George Hart, which were well-received as well.
Qiaochu Yuan over 11 yearsIs this limited to visual art? There are some interesting articles and books about the mathematics of Jorge Luis Borges' stories that might make for an interesting lecture.
Cheerful Parsnip over 11 yearsGood idea, Qiaochu.
Alp Mestanogullari over 11 yearsYou have the usual candidates, like the golden ratio. You can also tell a bit about the math of special effects/3D animation.
Mike Spivey over 10 years(I'm seeing your update now for the first time.) I'm glad the TSP art suggestion went over well!
Martin Sleziak over 7 yearsJudging from the fact that this is the oldest question in that tag, you were probably the creator of (art). I thought it might be polite to let you know about discussion on meta whether this tag is actually useful.
Bruno Stonek over 11 yearsJust for the record, that's not Spanish but Catalan.
Mike Spivey over 11 years@Bruno: Thanks. I will correct.
Peter Taylor over 11 yearsFWIW it's "and", not "in". And the title of the book (I presume - doesn't look like the name of a journal) is "Brief Journey to the world of Mathematics".
Mike Spivey over 11 years@Peter: Thanks for the translation.
uncle brad over 11 yearsYou certainly correct about there being too much material. You just need to pick something that speaks to you.
KCd over 11 yearsFrom the links provided, I would think the Mona Lisa picture is not really a solution to a TSP, but just an approximate solution. In any case, what does such work tell us about TSP or about the art being reproduced?
Mike Spivey over 11 years@KCd: It is a solution - just, as you said, not necessarily an optimal one. As I'm sure you know, TSP is a hard problem, and often the best we can do for large instances is to find a good approximately optimal solution.
Mike Spivey over 11 years@KCd: As to your question, I would say not much about the art being produced. Maybe it tells us something about TSP, but I'd have to read more on the subject to say what. I think of TSP art more as a curiosity that involves TSP and art rather than as something deep about TSP or art. I do think it is interesting, though, and that it would be worth at least a mention in a lecture to a general audience on art and math, which is why I posted it as an answer. :)