The shapes of surfaces captured the imagination and attention
of many mathematicians during the nineteenth century. To unfold the visual
secrets compressed and hidden within the shorthand of algebraic expressions, geometers
drew pictures, fashioned models, and even wrote manuals on how to visualize or
construct geometric forms.
These models and drawings were not only a source of pleasure
but also a valuable tool for probing a slew of exotic geometric structures.
Indeed, during the latter part of the nineteenth century, no university
mathematics department could count itself at the forefront of research and
pedagogy without owning a set of plaster models
depicting an array of geometric forms. Firms, particularly in Germany,
specialized in crafting these teaching aids.
Rudolf Clebsch's diagonal cubic surface.
Over the years, the models largely disappeared from view,
supplanted by more abstract representations and new directions in mathematical
research and pedagogical approach. More often than not, they ended up gathering
dust in closets or simply in the trash.
I was reminded of this history on a recent visit to the mathematics department at the University of
Nebraska in Lincoln. Retrieved from storage and exhibited in illuminated display
cases, these models now serve as a link between the rich early history of geometric
visualization and modern, computer-based approaches to representing the
intricacies of geometric forms.
You can find collections and displays of plaster
mathematical models at a number of universities, including the University
of Illinois at Urbana-Champaign, University
of Arizona, HarvardUniversity, Hebrew
University of Jerusalem, and others. The
original, hand-crafted models are also being recreated using digital
fabrication technology (see http://vimeo.com/18819673)
and inspiring the work of artists (see http://www.sugimotohiroshi.com/MathModel.html).
These graceful plaster models bring together the logically abstract
and the visually concrete in mathematics. They are vivid testimonials to the
work of nineteenth-century geometers and to the beauty of mathematical forms. They
represent elegant milestones in the struggle by mathematicians to elucidate the
fundamental principles of geometry.
References:
Fischer, G. 1986. Mathematische
Modelle: Mathematical Models from the Collections of Universities and Museums , Vol. 1. Vieweg & Sohn.
Peterson, I. 1990. Islands
of Truth: A Mathematical Mystery Cruise. W.H. Freeman.
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