Mathematical objects cannot be directly perceived through
our senses. Therefore problems arise when mathematics is to be taught
or disseminated. However, students (and mathematicians) usually use external
representations (as for example words, schemas, figures, symbols, gestures,
tools) when dealing with mathematical objects. A blackboard covered in
formulae is a commonly shared image reminding of a mathematics lesson.
However mathematical activity has always included manipulation of instruments,
as for example ruler and compass. The Laboratory of Mathematics of the
University of Modena owns a collection of about 200 geometrical mechanisms
(mathematical machines) that have been reconstructed on the basis of original
historical documents. The majority of the machines date back to the 17th-19th
century (e.g. perspectographs, curvigraphs pantographs for transformations),
but there are also some mechanisms dating back to antiquity, concerning
conic sections and the solution of problems.
The Laboratory in Modena has already prepared a number of exhibitions (Modena 1992 e 1998; Torino 1996; Cesenatico 2000; Treviso e Cesena 2002, Firenze 2002) and some limited thematic exhibitions during the week for the Scientific Culture and during seminars and conferences for teachers. In particular, in the year 2001 the section Perspective and Anamorphosis was presented in Modena within the Apriti Sesamo exhibition, at the Foro Boario. Different parts of the collection have been exhibited in European (France, Germany, Spain, The Netherlands) and non-European countries (USA, Canada, Mexico, Brasil, Japan). Complex models were constructed for Italian (e.g. the Citta' della Scienza in Naples) and foreign (Amsterdam, Grenoble, Bordeaux and Mexico City) Scientific Institutions.
The collection of machines is called Theatrum Machinarum. The catalogue
(updated until 1999) is on the web (http://www.museo.unimo.it/theatrum/)
and is available also on a CD (that can be requested to the Laboratory).
A CD about Perspective, drawing on the exhibition Perspectiva Artificialis,
is in preparation and will be available in April 2003.
The machines have been reconstructed with a didactical aim in mind.
The research activity of the Laboratory has been presented in many national
and international conferences. They were invited to two international
conferences, presenting work about curvigraphs and pantographs and about
The activity of the laboratory is co-ordinated by Prof. Mariolina. Bartolini Bussi, and organised by four teachers (Annalisa Martinez, Marcello Pergola, Marco Turrini and Carla Zanoli) and a contract researcher (Michela Maschietto).
Università di Modena e Reggio Emilia
Tel. 059 205 5176