古代ローマ・パンテオンの幾何学的比例について : 設計図法の考案とその適用に関する研究

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Since the Pantheon is very important as a prototype of western masonry and a source of design, it has been studied frequently during the Renaissance. The lively interest in antiquity during this period produced directly and indirectly a spate of sketches and studies of the building. However, the fundamental ratio for the building is still obscure. It is true that the geometrical figure on which the rotunda was based is spherical and very simple-as the Renaissance architects realized-. Thus one expects that the key to an understanding will be easily found. But the problem is not as easy as that. Francois Blondel (1617-1686) was among the very first to publish studies of the Pantheon's composition and shape. But Blondel's conceptions are not tenable. The incorrect results are due among other things to the fact that the drawing materials available to Blondel contained certain faults and were imperfect in various ways. In recent years, several additional works have been published. One of these is George Lesser's Gothic Cathedrals and Sacred Geometry (1957), which gives an interesting analysis of the proportioning of the Pantheon (pp.23-26 and pl.19). However, because of the deficiencies in Lesser's drawings, his results are incorrect. Kjeld de Fine Licht analysed the composition of the rotunda in his The Rotunda in Rome, 1966. (pp.194-198 with two figures). In his analysis, he produces two 16-sided figures inscribed within the basic circle following the inner face of the dome. The points of the teeth where the sides of two 16 side-figures intersect mark the outer periphery of the rotunda. This analysis is very complicated. He himself said, "It seemes impossible to demonstrate any simple and exact geometrical connection between the basic circle and the thickness of the wall". In this paper I am glad to state that I have discovered the geometrical rule which determines the wall thickness of the Pantheon. This can be done with the following procedure : first, I draw the square incribed in the basic circle, then I draw the smaller circle inscribed in this square. Consequently, a doughnut-like discrepancy results between the smaller circle and the basic circle. This discrepancy is 2-√<2>/4 S (S=span). If the span is 43.251 m, 2-√<2>/4 S is 6.33 m, which equal to a little bit more than the wall thickness of the rotunda. Furthermore, I have devised a method for deciding the dome shell thickness, the angle of inclination of the outer place of the haunch, and the inner diameter of the oculus by using a similar geometrical figure. I believe that this geometrical rule may have been used by the builder of the Pantheon.
1986-07-30

古代ローマ・パンテオンの幾何学的比例について : 設計図法の考案とその適用に関する研究

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