Perspective has been an important encounter between arts and mathematics which has turned out to be quite fruitful. The introduction of perspective into painting, which was the result of a long process aimed at finding out an effective way of representing scenes and objects realistically, lead to Renaissance painting which started in Italy and very soon spread all over Europe. On the other hand, perspective brought into mathematics the seeds of a process, which matured at the beginning of. XIX century, that led to projective geometry. After a brief overwiew on the origins of perspective, in which we illustrate the principle of intersection of the visual pyramid on which it is based, and starting from this simple principle, this paper gives a simple system of perspective representation through the "power" of the basic notions of the double projection of Monge, and then "gets to discover" its fundamental properties and concepts (such as vanishing points, horizon line, etc.) thanks to the dynamism of Cabri (software purposedly created for teaching geometry). This way it is possible to illustrate: (1) the genesis of the rules that are at the basis of various systems of perspective representation; (2) the origin of the concepts of improper point and improper straight line which, together with the operations of projection and section, are at the basis of projective geometry. The study includes considerations on geometry (homology and conics) and applications (perspective restitution).
|Data di pubblicazione:||1999|
|Titolo:||La Prospettiva: il punto di vista della Geometria|
|Nome editore:||Pitagora Ed.|
|Pagina iniziale:||pp. XVI+120|
|Appare nelle tipologie:||Monografia/Trattato scientifico|
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