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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.

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Is 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. –  Qiaochu Yuan Jan 28 '11 at 22:12
    
Good idea, Qiaochu. –  Grumpy Parsnip Jan 28 '11 at 22:40
    
You have the usual candidates, like the golden ratio. You can also tell a bit about the math of special effects/3D animation. –  Alp Mestanogullari Jan 29 '11 at 0:17
    
(I'm seeing your update now for the first time.) I'm glad the TSP art suggestion went over well! –  Mike Spivey Oct 12 '11 at 16:24

6 Answers 6

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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.

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You certainly correct about there being too much material. You just need to pick something that speaks to you. –  uncle brad Feb 2 '11 at 17:43

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." :)

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Just for the record, that's not Spanish but Catalan. –  lentic catachresis Jan 28 '11 at 22:04
    
@Bruno: Thanks. I will correct. –  Mike Spivey Jan 28 '11 at 23:58
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FWIW 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". –  Peter Taylor Jan 29 '11 at 9:43
    
@Peter: Thanks for the translation. –  Mike Spivey Jan 29 '11 at 14:43

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:

http://maa.org/news/092310Crannell.html

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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:

http://www.cgl.uwaterloo.ca/~csk/projects/tsp/

http://www.oberlin.edu/math/faculty/bosch/tspart-page.html

http://www.tsp.gatech.edu/data/art/index.html

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.

Mona Lisa

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From 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? –  KCd Feb 2 '11 at 17:58
    
@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 Feb 2 '11 at 18:59
    
@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. :) –  Mike Spivey Feb 2 '11 at 19:00

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/

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The golden ratio in architecture. I saw an interesting talk on this at Union College. They're fond of the golden ratio because of the Nott Memorial. There are a number of ratios, e.g. diameter to height, that approximate the golden ratio. The ratio is also incorporated into the design of the Gothic arches.

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