We take under consideration two masonry domes built during Italian Renaissance: the Santa Maria del Fiore dome in Florence by F. Brunelleschi and St. Peter's dome in Rome by Michelangelo. No original computation is known currently in reference to neither one nor the other. However present mathematical computations show that, even though probably unconsciously, the designs of both the domes were inspired by the use of catenary, a trascendent mathematical curve with excellent stability properties. It was defined and studied in details by Leibniz and Bernoulli brothers at the end of the 17th century (within the context of rising differential geometry) a long time later than both the domes were completely built. Therefore the two considered domes suggest that some practical applications of differential geometry in architecture design can be considered foregoing its theoretical formalization. Here we show some numerical computation which support this hypothesis. The aim of this work is to show that knowledge quite often is created in processes and not invented in a moment; in particular here we focus on the development of differential calculus related to its applications to equilibrium of masonry domes.

The relevant role of calculus in renaissance domes' design, before differential geometry was born

Pavani R.
2020

Abstract

We take under consideration two masonry domes built during Italian Renaissance: the Santa Maria del Fiore dome in Florence by F. Brunelleschi and St. Peter's dome in Rome by Michelangelo. No original computation is known currently in reference to neither one nor the other. However present mathematical computations show that, even though probably unconsciously, the designs of both the domes were inspired by the use of catenary, a trascendent mathematical curve with excellent stability properties. It was defined and studied in details by Leibniz and Bernoulli brothers at the end of the 17th century (within the context of rising differential geometry) a long time later than both the domes were completely built. Therefore the two considered domes suggest that some practical applications of differential geometry in architecture design can be considered foregoing its theoretical formalization. Here we show some numerical computation which support this hypothesis. The aim of this work is to show that knowledge quite often is created in processes and not invented in a moment; in particular here we focus on the development of differential calculus related to its applications to equilibrium of masonry domes.
AIP Conference Proceedings
Catenary, Funicular surface, Masonry domes, Mathematical knowledge development, Renaissance domes
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1207085
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact