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On the geometry and topology of Da Vinci domes

Nicolé Geyssel, María José Moreno, Andrés Navas

Abstract

We study the famous Leonardo Da Vinci's domes, as well as the variations invented by Rinus Roelofs, from a mathematical viewpoint. In particular, we consider the problem of closing the dome in order to produce a spherical structure. We explain why this problem is related to subtle geometric and topological considerations. This is in contrast with the 1-dimensional analog structure, namely Da Vinci's bridge, that can be easily closed up to make a circular shape.

On the geometry and topology of Da Vinci domes

Abstract

We study the famous Leonardo Da Vinci's domes, as well as the variations invented by Rinus Roelofs, from a mathematical viewpoint. In particular, we consider the problem of closing the dome in order to produce a spherical structure. We explain why this problem is related to subtle geometric and topological considerations. This is in contrast with the 1-dimensional analog structure, namely Da Vinci's bridge, that can be easily closed up to make a circular shape.
Paper Structure (7 sections, 10 equations)

This paper contains 7 sections, 10 equations.

Table of Contents

  1. Introduction
  2. The Da Vinci bridge
  3. The Da Vinci domes
  4. Da Vinci patterns and sphericity
  5. A warning on collinearity of vertices along rods
  6. Da Vinci meets Euler: exploring topology
  7. Conclusions