The Bridges is an international conference and festival on mathematics, music, art and architecture, held annually since 1998 at different locations. The conference attracts international scientists and artists who not only present their achievements in their particular disciplines, but also share the ideas and build bridges between mathematics, music, art, architecture and culture. This year the conference took place at the University of Coimbra, the most ancient university in Portugal and the third oldest university in Europe. The region is famous for its ceramics, and the university museum’s collection includes plates dating back to the seventeenth-eighteen centuries depicting graphs and formula copying pages from mathematics, astronomy and physics books. These plates once served as decorations in the University’s dining halls and students’ dormitories to help them study even at dinner and in their sleep!
Conference organisers Reza Sarhangi and Carlo H. Séquin invited more than a hundred and fifty lecturers, and exhibition curator Robert Fathauer presented works of seventy artists investigating beauty of mathematics and mathematical precision of art. Bridges participants had to choose between attending the lectures, solving mind-game puzzles, exhibitions, sharing and adopting pedagogical practises, listening to mathematical poetry and music and watching mathematical movies.
Among the participants of the conference there were specialists in a wide range of the disciplines: mathematicians, physicists, computer engineers, artists, designers, sculptors, architects, photographers, poets, dancers, musicians, each one with unique ideas for correlating mathematics and arts. For example, Ruth Mateus-Berr with colleagues created avant-garde clothes in Thinking LAB computer program by rotating forms of platonic solids’ conic sections, and E.S. Hur and B.G. Thomas used modular systems of geometric shapes uniting hundreds of felt circles into mosaic scarfs, shawls, and dresses.
A number of works were inspired by folk and indigenous art: Paulus Gerdes studies mathematical principles interwoven in the artistic decoration of basketry from various regions of Mozambique, Jim R. Paulsen creates abstract sculptures inspired by the culture of native North Americans, B. Lynn Bodner analyses repeating units in the Uzbek ornaments of the sixteenth century, and Jean-Marc Castera investigates Islamic pentagonal and diamond patterns.
Predictably, a number of works concern the beauty of fractals. Vincenzo Iorfida, Marcella G. Lorenzi and Mauro Francaviglia proclaimed the ‘aesthetic beauty of Fractal’ to be a modern artistic code providing creativity for ‘mathematically minded’ artists. Craig S. Kaplan demonstrated self-similar curves generated by a computer program from an arbitrary smooth curve. Stanley Spencer creates three-dimensional fractals folding and unfolding simple modules of platonic solids. Mehrdad Garousi and Hamed Akbari present a three-dimensional-like representation of Serpinsky triangle. Robert W. Fathauer makes naturalistically looking fractal trees in a wide range of fractal parameters, and Boris Kerkez works on the Mandelbrot Sound Map computer program transforming visual fractals into musical sequences. Fractal-like images were created by hand too: during one of the workshops, Mary Wahr taught the participants to the Decalcomania technique consisting of putting paint or ink on a smooth surface pressed tight with another surface thus producing fractal-looking patterns.
The work of a novice in mathematical art, Dmitry Kozlov, was the most successful among the experienced Bridges’ participants. He knots simple wire into self-forming three-dimensional figures: elliptical or hyperbolical, or quite surprisingly elliptical and hyperbolical in turns.
In addition to lectures and art exhibition, Bridges’ activities included demonstrations of many amazing mind-games, puzzles and construction sets. The authors were at the tables by their brainchildren, ready to answer questions concerning the rules of the games and their hidden mysteries.
The workshops were possibly the most interesting part of the conference. Mathematical artists deal with an amazing range of materials. Nicholas Durnan works with alabaster: during his two-hour workshop he has taught kids and adults to make toris, spheres, ovoids and Moebius strips by carving and polishing this soft material. Samuel Verbiese discussed the structures of ancient labyrinths starting from the Chartres labyrinth (created circa 1200) and reproduced them… on an orange’s surface!
Chern Chuang, Bih-Yaw Jin and Chia-Chin Tsoo applied traditional beading techniques to build computer models of a hundred atom’s molecules, while Mike Naylor and Vi Hart plaited hands, arms, legs and whole bodies of the participants into ornaments, polyhedron and even some iterations of Serpinsky triangle during their workshop ‘Geometry of human body’!
David M. White and Alexei Kolesnikov applied mathematical structures to theatrical performances from two points of view: of a mathematician and of a playwright. Susan Gerofski shared her experience of teaching mathematics in improvisational drama lessons where students played the habitants of a seismic region or partisans deciphering codes to communicate in an occupied country. Slavik Jablan and Kristóf Fenyvesi held a workshop in op-art folding projections of a four-dimensional cube into a mobile lattice.
Fernando Blasco followed Girolamo Cardano and Martin Gardner in demonstration of mathematical card tricks. He also demonstrated and explained tricks on sum prediction, rings and ropes focuses and more. At least two lessons concerned geometrical origami: Nick Fout and Jenn Marker taught to fold a piece of paper into a cube or a regular stellate icosahedron by the method invented by a Japanese master Sonobi, and Krystyna and Wojciech Burczyk showed their twisted-paper polyhedrons which look more like fairy-tale flowers.
Eva Knoll and Wendy Landry taught participants how to weave paper into various tessellations in a way a kindergarten child would understand, and Elaine Krajenke Ellison based her workshop on mosaic building on the Bhaskara’s (1114-1185) proof of the Pythagorean theorem. During two hours of the Bridges short movies festival, the audience enjoyed watching films of the very different techniques: from a simple cartoon about palindromic personages by Vi Hart and poetry-musical performance on the Pythagoras school by Rosanna Iembo and Irene Iaccarino, up to breathtaking kaleidoscopes by Curtis Palmer, three-dimensional fractals by Mehrdad Garousi and fractal kaleidoscopes by Vladimir Bulatov, and even more fascinating musical fractals by Harlan Brothers and Teja Krasek.
During the five day conference, a sculpture called Pentigloo, designed by French artist Fabien Vienne, was being built at the university museum square. A team of artists lead by Paul Hildebrand arrived to Bridgeso produce the sculpture, consisting of 44 000 elements of Zometool constructor set, . With the help from volunteers from the number of Bridges participants and guests they finished the sculpture at 2 am of the last night of the conference! It was indeed an inspiring process especially when construction was finished, and fragile legs of the sculpture held its 200 kg weight at the top of the university museum square, above ancient Coimbra, as a reminder of the wonderful festival of mathematics and arts.
Bridges 2011 Conference Materials were published in a 700-pages proceedings. Art works were presented in a 100-pages catalogue and on the web-site: http://gallery.bridgesmathart.org/exhibitions/2011-bridges-conference
Festival movies can be seen at http://bridgesmathart.org/past-conferences/bridges-2011/2011-short-movie-festival
Bridges 2012 will be held in Baltimore, USA.
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