The thesis is devoted to specific models of domes, of particular monumental importance, in which the geometric genesis has a special cultural and constructive role. The spherical geometry research, which made possible the celestial (time) and terrestian (space) measurements in the past, produced many assumptions, theorems and models. Particular relevance have had issues related to central projection. The architecture has followed the scientific research on these topics, essential to the society of the time, erecting with exemplary models. The cross-section shape of the Pantheon’s coffers is closely related to the stereographic polar projection, and the procedures for overturning the various planes of the sphere onto meridian plane, described by Ptolemy. The three domes designed by Filippo Brunelleschi for the Pazzi Chapel, although not made by him, have different geometrical genesis and all linked to a different interpretations of the sphere. The umbrella vault, particulary, reveals a very curious shape. It’s obtained by a three-dimensional transformation of a torus surface, with respect to the fixed point (dome’s oculus) and constant lenght (torus radius), like the concoid of Nicomedes in 2d. A very particular design choice, may have found the nutrients in scientific thought. In that particular moment, the Ptolemaic model of the universe was showing its weaknesses, and the proposals which would remove them speculates the planetary motions, which generates dynamic figures. The fact that the apparently complex motions of the planets could be actually very simple if observed from another point; could be easily intuited by Brunelleshi. The same rules, as ones used to generated pictures in central projection, were designing the orbits in our sky. The shape of the sail, which to an observer on the “ Earth “ (floor) shows all its complexity, seen from the “Sun” (oculus) reveals its simple geometry, not unlike a torus.

La proiezione centrale nel pensiero scientifico. Dal Pantheon alla Cappella Pazzi / Nevena Radojevic. - (2014).

La proiezione centrale nel pensiero scientifico. Dal Pantheon alla Cappella Pazzi

RADOJEVIC, NEVENA
2014

Abstract

The thesis is devoted to specific models of domes, of particular monumental importance, in which the geometric genesis has a special cultural and constructive role. The spherical geometry research, which made possible the celestial (time) and terrestian (space) measurements in the past, produced many assumptions, theorems and models. Particular relevance have had issues related to central projection. The architecture has followed the scientific research on these topics, essential to the society of the time, erecting with exemplary models. The cross-section shape of the Pantheon’s coffers is closely related to the stereographic polar projection, and the procedures for overturning the various planes of the sphere onto meridian plane, described by Ptolemy. The three domes designed by Filippo Brunelleschi for the Pazzi Chapel, although not made by him, have different geometrical genesis and all linked to a different interpretations of the sphere. The umbrella vault, particulary, reveals a very curious shape. It’s obtained by a three-dimensional transformation of a torus surface, with respect to the fixed point (dome’s oculus) and constant lenght (torus radius), like the concoid of Nicomedes in 2d. A very particular design choice, may have found the nutrients in scientific thought. In that particular moment, the Ptolemaic model of the universe was showing its weaknesses, and the proposals which would remove them speculates the planetary motions, which generates dynamic figures. The fact that the apparently complex motions of the planets could be actually very simple if observed from another point; could be easily intuited by Brunelleshi. The same rules, as ones used to generated pictures in central projection, were designing the orbits in our sky. The shape of the sail, which to an observer on the “ Earth “ (floor) shows all its complexity, seen from the “Sun” (oculus) reveals its simple geometry, not unlike a torus.
2014
Maria Teresa Bartoli
Nevena Radojevic
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/906761
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