By Eduard Casas-Alvero, Gerald E. Welters, Sebastian Xambo-Descamps

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**Extra resources for Algebraic Geometry. Proc. conf. Sitges (Barcelona), 1983**

**Example text**

Although Palladio claimed that "beauty will result from the form and correspondence of the whole with respect to the several p a r t s . . that the structure may appear an entire and complete body" [Wittkower, 1971], the limitation of these geometric progressions prevented him from achieving this worthy objective. 3) is never equal to another element of the progression. Thus the second canon of proportion fails and the system is limited in its application to proportioning only parts of the whole plan.

6), for the most part buildings and canvases of the Renaissance were organized by new principles of proportion based on commensurable ratios derived from the musical scale. 4 The Structure of Ancient Musical Scales The aspect of Greek writings that had the greatest influence on Renaissance architecture was the emphasis of Plato in Timaeus on the importance of the ratio of small integers. " These connections deeply influenced the neoplatonists of the Renaissance who felt that, as a result of this connection, the soul must have some kind of ingrained mathematical structure.

T i l i n g s of r e c t a n g l e s b y r e d a n d b l u e t i l e s , found in Le C o r b u s i e r ' s book Modulor [1968a]. 11 agree with the sum of the lengths across the bottom edges. Also check the sum of the right and left edges for agreement. T h e Modulor s y s t e m is e x t r e m e l y v e r s a t i l e . O n c e a r e c t a n g u l a r a r e a h a s b e e n tiled b y t h e Modulor, t h e t i l e s c a n b e r e a r r a n g e d i n m a n y different w a y s to form n e w t i l i n g s of t h e r e c t a n g l e .