Abstract
The relationships between art and geometry were not always the same, and this might be explained from the great differences between artistic styles and the way in which art has been socially considered, that profoundly changed through the centuries, alongside the development and evolution of the knowledge on geometry. The complexity of these relations may be found in the history of geometry itself, as well as in the structure and the way in which the professional and academic institutions work, not only in regard to their practice, but also to their learning systems. On this subject, a number of examples are considered to demonstrate the connection between the knowledge on geometry and its incidence or application in the works of art. One of these refers to the representation of the human figure, since the proposals to establish the standards of beauty span from the Classic Greece, until the development of contemporary anthropometry.
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Notes
- 1.
Goya’s letter has been published within the following exhibition’s catalogue: Renovación. Crisis. Continuismo. La Real Academia de Bellas Artes de San Fernando en 1792. Madrid: R. A. de BB. AA. de San Fernando, 1992.
- 2.
The best study on the foundation and the first years of the Real Academia de Bellas Artes of San Fernando is still the French Hispanist Claude Bédat’s doctoral thesis, published in French in 1973 and translated into Spanish for the edition quoted in the previous footnote.
- 3.
In a well-documented work by Alicia Quintana Martínez, about the San Fernando Academy, a part of it is dedicated to the publication that collects the “imparted subjects. The development of textbooks”. There, testimonies about mediocrity and the frustrated commitments pursued by the editorial policy of the Academy are described and analyzed in Quintana Martínez, Alicia. La arquitectura y los arquitectos en la Real Academia de Bellas Artes de San Fernando 1744–1774. Madrid: Xarait, 1983, pp. 64–75.
- 4.
Non-Euclidean geometries are primarily associated with names like Carl Friedrich Gauss (1777–1857), Nicolai Ivanovich Lobachévski (1792–1856) and Janos Bolyai (1802–1860), without forgetting pioneers like Girolamo Saccheri (1667–1733), Johann Heinrich Lambert (1728–1777) or Adrien Marie Legendre (1752–1833).
- 5.
An interesting and well-documented article in where this question is approached is Ruiz de La Rosa, José A.” Geometriai fabrorum” o la antítesis de las teorías sofisticadas” in Boletín Académico nº 7, octubre 1987.
- 6.
The Elements, on the contrary of what happens with other languages, has not received a complete translation into Spanish until very recent times. This circumstance was compensated with the quality and care of the three volumes edition published in [3].
- 7.
Context and references to the publication of this work have been studied in López Piñero, José María (1979) Ciencia y técnica en la sociedad española de los siglos XVI y XVII. Barcelona: Labor, p. 176.
- 8.
Among other titles, we can quote: La Rocha: Geometría y traza… de sastre…, 1618; Anduxar: Geometría y trazas pertenecientes al oficio de sastre, 1640.
- 9.
A Spanish translation of Dürer’s geometry treat exists: Instituciones de Geometría. México: Universidad Nacional Autónoma, 1987.
- 10.
A facsimile edition of Monge’s Descriptive Geometry exists, which contains a rigorous study by: Gentil Baldrich and Rabasa Díaz, “Sobre la Geometría descriptiva y su difusión en España”, in: Gaspard Monge. Geometría Descriptiva. Madrid: Colegio de Ingenieros, Canales y Puertos, 1996.
- 11.
Even if the work’s title is misleading, since the actual conception about delineation is associated with a profession or trade, it refers here to an abstract question related to mathematical nature when it speaks about “lines related”. Thus, this work must be understood as a “lines’ treatise”. Gómez Santa María, Agustín, Tratado de Delineación. Madrid, Pedro Mora, 1845.
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Gelabert, L.C. (2020). Geometry and Art. In: Viana, V., Murtinho, V., Xavier, J. (eds) Thinking, Drawing, Modelling. Geometrias 2017. Springer Proceedings in Mathematics & Statistics, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-030-46804-0_4
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