On the geometry and topology of Da Vinci domes

Autores/as

  • Nicolé Geyssel Universidad Técnica Federico Santa María
  • María José Moreno PUC
  • Andrés Navas Universidad de Santiago de Chile

DOI:

https://doi.org/10.33044/revem.44901

Palabras clave:

Leonardo Da Vinci, Bridge, Dome, Geometry, Topology

Resumen

We study the famous Leonardo Da Vinci’s domes, as well as the variations pursued 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.

Descargas

Los datos de descarga aún no están disponibles.

Referencias

Aigner, M., y Ziegler, G. M. (1998). Proofs from the book. Springer Verlag.

Brasó, E. (2018). Les cúpules de Leonardo da Vinci. Noubiaix, 42, 116–126.

Carrasco, P., Carvacho, M., y Sánchez, F. (2023). Cúpulas de Da Vinci: la geometría colaborando con otras disciplinas. En J. Huinacahue y D. Soto (Eds.), Educación Matemática Insterdisciplinar en el Aula. Ediciones UCM.

Duvernoy, S. (2008). Leonardo and theoretical mathematics. Leonardo da Vinci: architecture and mathematics. Nexus Netw. J., 10(1), 39–49.

Humenberger, H. (2021). Mathematische Aktivitäten rund um die LeonardoBrücke. En Schriftenreihe zur Didaktik der Mathematik der Österreichischen Mathematischen Gesellschaft (Vol. 45, pp. 67–86).

Lemmermeyer, F. (2016). Leonardo da Vinci’s proof of the Pythagorean theorem. College Math. J, 47(5), 361–364.

Navas, A. (2019). Une ≪erreur ≫ géométrique dans la ligue des champions. Images des Mathématiques, CNRS.

Roelofs, R. (2008). Two- and three-dimensional constructions based on Leonardo grids. Nexus Netw. J., 10(1), 17–26.

Schattschneider, D. (1978). The plane symmetry groups: their recognition and notation. Amer. Math. Monthly, 85(6), 439–450.

Scott, P. (2006). Angle defect and Descartes’ theorem. Australian Mathematics Teacher, 62(1), 2–4.

Song, P., Fu, C.-W., Goswami, P., Zheng, J., Mitra, N. J., y Cohen-Or, D. (2013). Reciprocal frame structures made easy. ACM Transactions on Graphics, 32 (Issue 4, 94), 1–13.

Descargas

Publicado

2024-04-30

Número

Sección

Artículos de Matemática