Abstract
Starting from the impact, which the École Polytechnique had on higher educations in Europe, this paper wants to highlight the role of material models especially for teaching mathematics. Models of ruled surfaces play a prominent role in this narrative, since Gaspard Monge, who taught “Géometrie descriptive” in Paris between 1794 and 1816, already used string models to support his lectures. For this reason, we want to trace especially the history of ruled surface models from the late 18th century to the presence. The investigation focuses on persons, used materials and the major topics. It is known that the axiomatization of mathematics lead to a decay of the meaning of material models in the early 20th century. But at the same time, material mathematical models gained relevance in other disciplines like civil engineering and art. We also want to show, how ruled surfaces can be part of current teaching projects.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
VIAF: 41838958.
- 2.
VIAF: 22146457.
- 3.
VIAF: 24639786.
- 4.
VIAF: 61582661.
- 5.
VIAF: 71489420.
- 6.
VIAF: 12439831.
- 7.
VIAF: 69046313.
- 8.
VIAF: 113316205.
- 9.
VIAF: 221469987.
- 10.
VIAF: 14854402.
- 11.
VIAF: 66532326.
- 12.
VIAF: 26070333.
- 13.
VIAF: 40131621.
- 14.
VIAF: 24603438.
- 15.
VIAF: 32743840.
- 16.
VIAF: 302409209.
- 17.
VIAF: 67221043.
- 18.
VIAF: 85973061.
- 19.
VIAF: 315114415.
- 20.
VIAF: 69705881.
- 21.
VIAF: 42638020.
References
Boyer, C.: History of Analytic Geometry, p. 189. Dover Publications Inc. ISBN: 978-0486438320
Meyer, W.F., Mohrmann, H.: Encyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Dritter Band in drei Teilen. Geometrie. Zweiter Teil. Erste Hälfte, pp. 188 and 189. ISBN: 978-3-663-15460-0
Lordick, D.: Intuitive design and meshing of non-developable ruled surfaces. In: Proceedings of the Design Modelling Symposium, Berlin, pp. 248–261 (2009)
Rowe, D.: Mathematical models as artefacts for research: Felix Klein and the case of Kummer surfaces. Mathematische Semesterberichte. Springer (2013). ISSN: 1432-1815
Monatsberichte der Königlichen Preußischen Akademie der Wissenschaften zu Berlin. Aus dem Jahre 1863. 26. NOV. Gesamtsitzung der Akademie, p. 539
A catalogue of a collection of models of ruled surfaces, constructed by M. Fabre de Lagrange. https://archive.org/stream/catalogueofcolle00fabrrich
Catalog mathematischer Modelle für den höheren mathematischen Unterricht. Siebente Auflage (1911). Martin Schilling
The Encyclopedia Britannica. Vol. XV. Mathematical Drawing and Modelling. pp. 628 and 629
Lordick, D., Klawitter, D., Hagemann, M.: Liniengeometrie fr den Leichtbau. In: Scheerer, S., Curbach, M. (eds.) Leicht Bauen mit Beton. Forschung im Schwerpunktprogramm 1542, pp. 224–235. Frderphase 1., Dresden (2014)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Päßler, R., Lordick, D. (2019). Material Models of Ruled Surfaces as Witnesses to the Development of Mathematical Teaching. In: Cocchiarella, L. (eds) ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics. ICGG 2018. Advances in Intelligent Systems and Computing, vol 809. Springer, Cham. https://doi.org/10.1007/978-3-319-95588-9_182
Download citation
DOI: https://doi.org/10.1007/978-3-319-95588-9_182
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-95587-2
Online ISBN: 978-3-319-95588-9
eBook Packages: EngineeringEngineering (R0)