HONR229P: Mathematics and Art

Fall 2004

Professor: Niranjan Ramachandran 4115 Mathematics Building, 5-5080, [email protected] Office Hours: Tuesdays 2pm - 4pm.

Class meets Tuesdays and Thursdays 12:30pm-1:45pm in Math Building 0401.

Course page: www.math.umd.edu/~atma/Doc1.htm

Course description: The aim of this course is to introduce students to the interactions, interrelations, and analogies between mathematics and art. Mathematicians (and scientists, in general) are in search of ideas, truth and beauty, not too different from artists. Our task will be to see the parallels between the viewpoints, the inspirations, the goals of (and the works produced by) artists and scientists. We shall begin with examples from history of art (such as the theory of perspective due to Leonardo da Vinci), works of art (such as Durer's Melancholia, Escher’s Waterfall), architecture (Parthenon, Le Corbusier) to illustrate the impact of mathematics on art. Of special interest to us will be the period of the Italian Renaissance and also the early part of the 20th century (the new viewpoint on space-time). The affinity of music with mathematics will also be explored (as in the music of Bach, or the foundations of tone, the role of harmony). We shall then talk about beauty in mathematics; this will be amply illustrated with examples from the history of mathematics. Emphasis will be put on the aesthetic aspect of things. We will even see how truth and beauty come together in a beautiful proof. All through the semester, we will be comparing and contrasting the two subjects. Hopefully, by the end of the semester, one's sense of beauty will be enriched also to appreciate beauty in the world of mathematics.

Books: (There will also be other material handed out in class.) (a) Keith Devlin, Mathematics: the science of patterns. (b) Georges Ghevergese Joseph, The crest of the Peacock (c) Daniel Pedoe, Mathematics and the visual Arts (d) Douglas Hofstadter, Godel, Escher and Bach. (e) Robert Pirsig, Zen and the art of motorcycle maintenance. (f) Jerry King, The art of mathematics. (g) Walter Pater, The renaissance. (h) Subrahmanyam Chandrasekhar, Truth and Beauty.

(It is not necessary to buy all of these but the first three cover much of the relevant ground; I will put all these books on reserve at McKeldin library for the course. There are also lots of material available online which is impossible to list here..I urge you to Google ``Mathematics and Art''.

Plays: Tom Stoppard, Arcadia. Tom Stoppard, Rosencrantz and Guildenstern are dead. Michael Frayn, Copenhagen. Joanne Sydney and Joshua Rosenblum, Fermat’s Last Tango.

Useful periodicals: American Mathematical Monthly, The Mathematical Intelligencer, Mathematics Magazine, Scientific American.

Course Format and Grading: There will be reading assignments and students are supposed to come prepared to discuss them in class. There is an overabundance of reference material (see course homepage). In-class and out- of-class discussions are greatly encouraged. Most likely, there will be guest lectures and possibly even a field trip to a mathematical artist’s studio in Baltimore.

Specific requirements: • One half-hour in-class presentation. • One mid-term paper (5-8 pages). • Discussion Leadership (two themes): a team of two students lead/chair a discussion session for a half-hour. Each student will do this twice during the semester. The duties of the team include providing reading material for the class online (or make it available online – more details later), a question list (topics which will be discussed in class) for the reading, and then to actually chair the session. • Biweekly reports (1 page each): thoughts about the theme, reading and activities. • One final paper (10 pages): A substantial work requiring you to present an original line of thought pursued by yourself. You may use help from the internet and other reference material (referenced with credit, of course) as a springboard, but the jump should be your own! Clarity of thought, Originality, and Creativity stressed. Complements such as your own artwork and music related to the paper would be fantastic!

Presentation 100 Mid-term paper 75 Final paper 150 Discussion Leadership 100 Reports 75 Total 500

Many topics are possible for the term paper; here are -- but only a few -- suggestions: From "Leonardo da Vinci, the Renaissance human" to "The mathematics of snowflakes" to "How did Escher make his drawings" to "Why the second law of thermodynamics is beautiful" to "Comparison between the works of Newton, Shakespeare and Beethoven". It is best to choose a topic that is close to your actual interests.

Schedule: • Biweekly reports due on these days: 14 September, 30 September, 14 October, 28 October, 16 November, 2 December. • Mid-term paper due: 19 October • Final paper due: Noon on 10 December. • Presentations: November and December

Please keep visiting the course page for updates.

CORE: Mathematics and Sciences, non-lab [MS]