by Federico Fallavollita, Marta Salvatore
This paper aims to highlight the utility of the synthetic approach in solving geometry problems thanks to the contribution of new digital technologies. The synthetic approach, as is known, addresses geometry problems without recourse to analytical methods; especially for architects, the synthetic approach relies on drawing and models, 2D graphics yesterday, 3D digital graphics today. The digital revolution has brought significant changes to the study of geometry both in education, and in research. If, for a long time, the instruments were rulers and compasses, today the main tools are computers. Currently, we can draw directly into space with an accuracy never before achieved, and we can use, in geometric constructions, forms far more complex than those represented by ruler and compass. This has enhanced the heuristic capabilities of the synthetic approach. There is a vast repertoire of geometry problems belonging to the Monge school that, for several years now is no longer studied in engineering and architecture schools: however, in the light of new digital tools, it is still a precursor to new ideas for research. This contribution aims to show how this heritage can be updated and expanded through the digital synthetic method.
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by Riccardo Migliari, Jessica Romor, Marta Salvatore
Traditional teaching of perspective wants the perspective image to be generated with various procedures, which make use of the orthogonal projections of the object that is to be represented. It is nevertheless well-known that the perspective image also can be generated autonomously, that is to say, without resorting to the orthogonal projections, as part of a method known as ‘central projection’.
In many schools and in many textbooks these two paths, which both lead to the genesis of the perspective image, remain distinct, as if they were two different methods, if for no other reason than their vocation; the first, also called, improperly, ‘the architect’s method’, which only focuses on the achievement of the result: an image similar to the natural vision of the space; the second, conceptual, devoted to the study of the central projection in itself and its applications of projective nature: from the genesis of the quadrics to the homography.
In the Roman school, yet, as from the second half of the twentieth-century, it was attempted to bring together into one single method the two above-mentioned approaches to perspective, giving a happy ending to a history that for centuries has seen the perspective split between artists and mathematicians.
In this paper, after a short presentation of the characteristics of the ‘perspective as a representation method’, is highlighted the advantages of the aforesaid method in academic teaching. These are, precisely: first of all the possibility to see in the perspective the generalization of the representation methods, following on from the thought of Wilhelm Fiedler (1832-1912); then the possibility to easily add the concepts relating to infinity (points, straight-lines and the improper plane); and, the possibility to establish a relationship that is not general, but operational, between the graphical perspective and the digitally rendered perspective.
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This essay discusses the importance of didactics and the textbooks that represent the educational tool of it, being these an activity that is capable to integrate the results of research into the body of the Science to which they belong. The textbook, in fact, unrolls the leading thread of History while essays, articles and conference proceedings only shed light on a short stretch of that historical line. The essay also examines the possible criteria that permit to distinguish between a commercial publication and innovative works, which deserve no less attention than the results of scientific studies, transmitted in the manners that are exclusive of the academic communication.