Collected works with commentaries. Vol.3. The Hopf-Wiener by Norbert Wiener; Pesi Rustom Masani

By Norbert Wiener; Pesi Rustom Masani

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Additional resources for Collected works with commentaries. Vol.3. The Hopf-Wiener integral equation, prediction and filtering, quantum mechanics and relativity

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Of these, 130 have domes with an oval plan. Fig. 11a shows Chappuis’s classification of Romanesque ovals. Fig. 11b shows clearly the oval plan in two churches. Chappuis has found, then, a precedent in Europe for the Renaissance oval domes, which so far has not been noted by historians of architecture. Fig. 11. The oval form in French Romanesque churches [Chappuis 1976]. a) Classification of ovals; b) Two examples of churches with oval plans: above, SaintMartin de Gurçon, Dordogne, and below, Balzac, Charente Another element in which oval arches can be found in Romanesque churches are the groined vaults, resulting from the intersection of two barrel vaults.

In late Gothic, however, in England, Germany and Spain, the Gothic masters began to employ oval forms, generated by the tangency of circles of different radii. The first to note the employment of this kind of “oval” ribs was Willis [1843] (fig. 15). Again, the tradition was well known in the Orient. In the comprehensive study of Cejka [1978] on the use of the arch in Islamic architecture, there are many examples of the same kind of geometries, which predate the European by several centuries. The first documented evidence of the use of ovals is found in Germany.

This result is not completely original. In Milankovitch’s analysis, however, it takes a new light and becomes the basis for a critical review of previous studies on the line of thrust where the equation (10) V dy =0  H dx has been wrongly assumed as invariably true. 190 FEDERICO FOCE – Milankovitch’s Theorie der Druckkurven From the general to the particular: Application of the theory to particular cases of masonry vaults Starting from the general equation (9) Milankovitch discusses the following particular cases of geometry and load condition.

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