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In classical culture, architecture and mathematics were strongly connected by a parallel sense of beauty. The conceptual beauty of mathematical rules was echoed in the search for canons of beauty in art. Scientists and artists both pursued divine perfection. In his treatise titled De Architectura Libri Decem, the Roman architect-engineer, Marco Vitruvius Pollio, conveyed to the Renaissance the cultural background inherited from Classical culture, whose substance and values were in turn conveyed to posterity by the Renaissance humanists. For Vitruvius, beauty in architecture will originate from the numbers that the designer will carefully and knowingly choose while sizing the geometric shapes of the designed object: the numbers, their ratios, their proportion, their modularity, and their commensurability. Renaissance humanists also included in the many mathematically beautiful items the peculiar proportion that Euclid used to name the "extreme and mean ratio." The mathematician Luca Pacioli named it "the divine proportion." A further geometric form became essential to Renaissance architecture when, toward the end of the fifteenth century, a new diagram appeared in Italian religious architecture: the central plan. In centrally planned churches, the dome rises over the heads (and souls) of the worshippers, thus creating a different spatial relationship between the single individual and the house of God. The central space and its dome represent the Earth under the Heavens, with Man at the center of the universe. While these geometric forms and systems were embedded in architectural plans, the Renaissance is also the time in which the geometric rules for perspective representation were reinvented, thus providing designers with a new work tool.

DOI: 10.1007/978-3-319-70658-0_10-1

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