A. In this workshop the participants used dynamic geometry software to make geometric constructions that interpret and model some milestone constructions proposed in the history of geometry. Four topics (and corresponding sets of historical texts – English and French versions) were proposed for interpretation and modelling. The participants, working in small groups, had the possibility of choosing a topic to work on. Proposed topics and texts were the following:

1. Piero della Francesca (c. 1410-1492).

– « On the perspective plane, to draw in its place a given square area »; from the book

– De Prospectiva Pingendi (On perspective for painting), before 1482.

2. Albrecht Dürer (1471-1528) and Germinal Pierre Dandelin (1794-1847).

– Conic sections by double projection and Dandelin spheres.

– A. Dürer, text from the book Underweysung der Messung mit dem Zirckel und Richtscheyt. . . (Instruction in Measurements with Compass and Ruler in Lines, Planes and Solid Bodies), Nuremberg, 1525.

– G. Dandelin, text from the article « Mémoire sur l’hyperboloide de révolution, et sur les hexagones de Pascal et de M. Brianchon », Nouveaux Mémoires de l’Académie Royale des Sciences et des Belles-Lettres de Bruxelles, Classe de Sciences, 1826.

3. Gilles Personne de Roberval (1602-1675) and René Descartes (1596-1650).

– The tangent to the cycloid

– G. Roberval, text from the article « Observations sur la composition des mouvements et sur le moyen de trouver les touchantes des lignes courbes », Recueil de l’Académie, tome VI, 1693.

– R. Descartes, text from a letter to Père Mersenne (1638), Œuvres, t. II.

4. Gaspard Monge (1746-1818)

– Construction of the planes tangent to a sphere and containing a given line

– Text from the book Géométrie Descriptive, 1799.

B. Complete guidance and hints on the use of the software were given as handouts, computer files and direct help. The program The Geometer’s Sketchpad, version 4, was used in this workshop, but other dynamic geometry software (like Cabri) could be used later to solve the same questions. Two participation modes were possible in this workshop:

– if the participant had some experience in the use of The Geometer’s Sketchpad (GSP), he or she was able to try to interpret, through geometric constructions made with the GSP, the given texts, and in this way to construct a dynamic model corresponding to the instructions, results or problem solutions given by the mathematicians referred in each topic;

– if this was not the case, the participant was able at least to follow constructions, step by step, to solve or model the same problems or results, with the help of GSP documents included in the CD given to each participant.