Geordnete Verhältnisse. Mathematische Anschauungsmodelle im frühen 20. Jahrhundert

Abstract

Geordnete Verhältnisse. Mathematische Anschauungsmodelle im frühen 20. Jahrhundert Summary: Sorted Geometry. Mathematical Models on Display around 1900. By 1870, around the same time that mathematics turned away from intuitive Euclidean geometry, increasingly three-dimensional geometric models were being incorporated into mathematical education at German universities and technical colleges. Connected to the increasingly specialized nature of engineering education as well as the growing demand for students in the fields of mechanics, kinematics, and statics in 1900, mathematics education at all levels called for the inclusion of more practical applications, often via the use of objects or images. Examining the works of the Darmstadt-based professor of descriptive geometry Hermann Wiener , this essay discusses the various ways that three-dimensional mathematical models were presented -both in combination with text and image, as well as part of an arranged series of objects in a showcase. As a mathematics professor, Wiener dedicated himself to the construction and use of models. He produced several series of wire models and sold them with an accompanying catalogue containing price lists and images. The models and the images were explicitly meant to serve as tools for enhancing students' intuitive mathematical knowledge. The visual knowledge thus generated was therefore cultivated not only through the research style of professors, but also as a result of the way in which things were presented and shown in a variety of non-academic contexts around 1900, such as shop windows and exhibition showcases. This essay reveals that these various new ways of arranging mathematical models had an epistemic value that was deeply connected to visual concepts of that time period.

Paper, Plaster, Strings: Exploratory Material Mathematical Models between the 1860s and 1930s

“…25. Following (Sattelmacher 2013), one can suggest that since the models became merchandised and an object to consume, they lost their exploratory character.…”

Models illustrating a classification of plane cubic curves

“…In some cases this is accompanied by a drawing. Several texts describe the origin and development of this model making, for example (with a focus on the Göttingen collection) [16], and also [17] (mostly discussing H. Wiener's collection).…”