[Une diversité de visualisations et non-visualisations : points de branchement et courbes de ramification autour de 1900.]
This article deals with the different ways branch points and branch curves were visualized at the turn of the 19th century. On the one hand, for branch points of complex curves one finds an abundance of visualization techniques employed. German mathematicians such as Felix Klein or Walther von Dyck were the main promoters of these numerous forms of visualization, which appeared either as two-dimensional illustrations or three-dimensional material models. This plurality of visualization techniques, however, also resulted in inadequate images that aimed to show the varied ways branch points could possibly be represented. For branch (and ramification) curves of complex surfaces, on the other hand, there were hardly any representations. When the Italian school of algebraic geometry studied branch curves systematically only partial illustrations can be seen, and branch curves were generally made “invisible”. The plurality of visualizations shifted into various forms of non-visualization. This can be seen in the different ways visualization techniques disappeared.
L'article traite des différentes façons de visualiser les points et les courbes de branchement autour de 1900. De nombreuses techniques de visualisation ont été employées pour les points de branchement de courbes complexes. Des mathématiciens allemands comme Felix Klein ou Walther von Dyck ont été les principaux promoteurs de cette multitude de visualisations, que ce soit sous la forme d'illustrations ou de modèles matériels tridimensionnels. Cependant, cette pluralité de techniques a également été à l'origine d'images inadéquates visant à montrer les diverses manières possibles de représenter des points de branchement. Pour les courbes de branchement (et de ramification) de surfaces complexes, il est difficile de trouver une visualisation. Lorsque les courbes de branchement ont été systématiquement étudiées par l'école italienne de géométrie algébrique, seules des illustrations partielles ont pu être trouvées, et les courbes de branchement ont été généralement rendues « invisibles ». La pluralité des visualisations s'est transformée en une pluralité de non-visualisations, dont témoignent différents modes de disparition des techniques de visualisation.
DOI : 10.24033/rhm.224
Keywords: Visualization techniques, their disappearance, three-dimensional models, branch point, branch curve, ramification curve, algebraic geometry.
Mots-clés : Techniques de visualisation et leur disparition, modèles tridimensionnels, point de branchement, courbe de branchement et courbe de ramification, géométrie algébrique.
@article{RHM_2019__25_1_109_0,
author = {Friedman, Michael},
title = {A plurality of (non)visualizations: {Branch} points and branch curves at the turn of the 19th century},
journal = {Revue d'histoire des math\'ematiques},
pages = {109--194},
year = {2019},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {25},
number = {1},
doi = {10.24033/rhm.224},
mrnumber = {4028878},
zbl = {1458.14007},
language = {en},
url = {https://www.numdam.org/articles/10.24033/rhm.224/}
}
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Friedman, Michael. A plurality of (non)visualizations: Branch points and branch curves at the turn of the 19th century. Revue d'histoire des mathématiques, Tome 25 (2019) no. 1, pp. 109-194. doi: 10.24033/rhm.224
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