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Elegance at the Matemateca

Exhibition presents collection of interactive objects that represent mathematical equations, theorems and concepts

Chladni plates with sawdust forming patterns produced by vibration

Léo RamosChladni plates with sawdust forming patterns produced by vibrationLéo Ramos

When praising a specific accomplishment in their area, mathematicians like to use words like “beautiful” and “elegant.” The use of these adjectives may seem inappropriate to someone outside of that world, in which almost everything is abstract. “That is a misconception,” says Eduardo Colli, professor at the Institute of Mathematics and Statistics of the University of São Paulo (IME-USP). “We see mathematics as something colorful, beautiful, and malleable and not just a jumble of numbers and calculations.” The interactive exhibition Matemateca reflects that feeling. It is an exhibition of works that seeks to find a language made up of aesthetic objects to represent another language—mathematics.

The group led by Colli and Deborah Raphael, also from the IME, and also involving other professors, in addition to undergraduate and graduate students, began designing, prototyping and gathering objects in 2003 in order to promote the discipline in a concrete, interactive manner. “The language of mathematics is opaque and hinders access for most people,” says Raphael. “Our goal is to present the different facets of the field in a playful way.” One of the initial references was the French exhibition Maths 2000 at the City of Science and Industry, in La Villette Park, Paris. As ideas emerged, Colli and Raphael commissioned works from craftsmen and companies specialized in prototyping. Financial support for the project came from various parts of USP and from the National Council for Scientific and Technological Development (CNPq).

Objects with ruled surfaces, straight lines that form structures with curves

léo ramosObjects with ruled surfaces, straight lines that form structures with curvesléo ramos

Eleven years later they were able to gather and present the nearly 40 attractions, divided into groups such as shapes, movement and thinking challenges. The exhibition was held in the lobby of the USP administration building in São Paulo through December 12, 2014 and was visited by students of all levels.

The chaotic water wheel, a experiment consisting of an acrylic wheel mounted vertically, with various cups, was located near the entrance. As the water falls into the cups, the wheel turns either in one direction or the other, unpredictably. They used this device to illustrate the study of chaos, a subarea of dynamic systems—Artur Ávila, the Brazilian who won the Fields Medal, works in this area. “The wheel is interesting because it was made by an undergraduate class taking a multidisciplinary course taught by Deborah Raphael, Artur Simões Rozetraten, a professor at FAU [USP School of Architecture and Urban Planning] and me,” says Colli.

Chladni Plates are among the various curiosities exhibited. They are metal plates of various shapes covered with sawdust that, when “played” with a violin bow, emit musical notes. The vibration caused by the bow rearranges the sawdust and draws geometric figures on the plate. The experiment was first carried out about 200 years ago by German physicist and musician Ernst Chladni (1756-1827). “This problem has still not been definitively resolved in the literature,” says Raphael.

the chaotic water wheel

Léo ramosThe chaotic water wheelLéo ramos

Another curious exhibit has been called little swing by the curators, as it reminds them of the swings on children’s playgrounds. The exhibit contains a tray holding a sheet of paper. The swing is activated and a pen attached to a wooden arm is allowed to touch the paper. The movement of the swing leads to surprising drawings, similar to those available for computer screen savers. Variations of this structure, called a harmonograph, can be found on the Internet.

The part of the show dedicated to shapes is the most colorful and artistic. The objects in the Surface topology display illustrate the topological point of view, in which two surfaces are equivalent if they can be transformed into each other through deformations without breaking. One object, in the form of a mug, can be deformed until it becomes a doughnut, for example. The Ruled surfaces display contains curved surfaces composed entirely of straight lines. Various objects are used to exemplify these mathematical ideas, some of which represent equations. The principle of the ruled surface was used by Oscar Niemeyer when designing the Cathedral in Brasília.

The curators would like to have a fixed location for the displays at IME, but lack space. “For now, we have been able to display the exhibits in the corridors,” says Colli. Part of the main hall of the administration building holds another mathematics exhibit, Pourquois les mathématiques?, from the Maison des Mathématiques et l’Informatique in Lyon, France, developed in 2000.