Model of the 3rd-degree Cayley plane, maker: Bartholomeus Hendriks, 1887, ca. 42.0 × 32.0 × 27.2 cm, plywood, textile threads, paint. KIT Archives 28508/12.
“Descriptive geometry forms the basis of the entire education in graphics at the Polytechnical College,” this according to the school’s program from 1840. Over a period of two years, students were taught the fundamentals and skills of descriptive geometry in a series of courses. This specialized mathematical field focuses on the geometrical and constructive methods for projections of three-dimensional objects onto a two-dimensional plane. Practical courses complemented the theory, in which students built models based on mathematical textbook problems to visualize surfaces, curves, and sections described in theoretical terms. KIT has a collection of these thread models from the 1870s to the 1910s. Labels on some models indicate the specific problems and textbooks involved, with frequent references made to Christian Wiener’s textbook on descriptive geometry (1884–86) and Karl Rohn’s textbook dedicated to this branch of geometry (1901). Today, the tasks once solved by means of descriptive geometry are largely performed by computer. As a result, the focus of study has shifted toward mastering Computer-Aided Design programs and using them to solve complex problems. as, kn
Under the guidance of their teacher Christian Wiener, students at Karlsruhe Polytechnical College attended practical courses on models. Wiener was professor of descriptive geometry in Karlsruhe since 1852. In this subject, aspiring engineers learned how to design buildings and machines. It was a permanent part of basic mathematical education at technical educational establishments in the 19th century. The Karlsruhe models share a very distinctive style, varying in form and material with maker. Some models are made of wood, strung with threads, others have a metal frame. Some are filigree in design and remind one of Art Nouveau decorations, others rather resemble pieces made by a carpenter’s apprentice with functional frames. Many models bear the names of their makers — there is really no need to specify the gender here, because in this period students were without exception male. Seminars on making mathematical models were a typical component of technical courses of study during the 19th century. These courses served as exercises in geometric planar and orthogonal perspective, that is, the transposition of a three-dimensional object onto a two-dimensional drawing and vice versa. Very different materials were used in the process. Some models were molded by hand out of plasticine and subsequently cast in plaster; others were turned wood or were built of interlocking pieces of cardboard. Each material determined its own building technique. Models made of thread with a metal or wooden frame were made using readymade templates. Thread models like the ones in the Karlsruhe collection first evolved in Paris around 1830. The idea of depicting second-order surfaces by means of a metal frame with threads strung inside it originated from the mathematician Théodore Olivier, professor of descriptive geometry and cofounder of the École Centrale des Arts et Manufactures. Olivier wanted to train modern engineers, in other words, ones who knew how to find answers to the challenges of the industrial age. They had to work with materials that were also used in industry, for instance, metal or else glass and cement. In the collection that Christian Wiener had assembled, there were models not only of metal and thread, but also of entirely different materials, such as wood and plaster. His son Hermann Wiener (1857–1939) specialized himself wholly in models of one particular method of production. Hermann Wiener had studied with his father for two years in Karlsruhe, attending the model-building practical sessions and thus had learned how to depict second-order surfaces spatially. For that he exclusively used brass wire and silk threads. These wire and thread models, made up to the 1910s, were also considered “modern” because they were quite different from the material regularly used in model building: plaster, which by then was considered outdated. Consequently, thread models can be seen as modern in two respects. On one hand, with regard to the new challenges posed by industrial modernity, and on the other hand, for aesthetic reasons. One material (wire or metal) was superseded by another (plaster, cardboard) because of new conceptions about aesthetics and functionality. Hermann Wiener deemed plaster inferior because it replicated a geometrical surface too imprecisely. He expected a model to be simple and clear — which metal and threads could achieve particularly well. The possibility of expressing mathematical properties of a model by specific materials is characteristic of three-dimensional models. They cannot be realized in a computer and that is the intrinsic value of mathematical collections even now. Anja Sattelmacher