Models of Surfaces

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The 19th century was an extrordinary period in the history of geometry,featuring exciting, even revolutionary work by giants of geometry(such as Plucker, Riemann, Klein and Lie just to name a few), but also suffering from fragmentation and an extreme lack of consensus about whatshould be studied and how it should be studied.

One line of inquiry, pursued with great enthusiasm from the middle ofthe 19th century through the beginning of the 20th century, was the investigation and classification of cubic and quartic surfaces. The discoveryof the existence of 27 lines on a (nonsingular) cubic surface was hailedas a discovery of monumental importance and hundreds of papers were writtenabout cubic surfaces and their lines. Quartic surfaces emerged originallyfrom optics and were vigorously studied by Kummer, Klein, and many others.
During many of these investigations, models were built to illustrateproperties of these surfaces. The contruction and study of plaster modelswas especially popular in Germany (particularly in Gottingen under theinfluence of Felix Klein). Many of the models were mass produced by publishinghouses and sold to mathematicians and mathematics departments all overthe world. Models were built of many other types of surfaces as well, including surfaces arising from the study of differential geometry and calculus. Such models enjoyed a wonderful reception for a while, but after the 1920's production and interest waned.

 


 

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Please come to my new home at http://math.harvard.edu/~angelavc/models/


URL of this page: http://math.bu.edu/people/angelav/projects/models/summary.html
Angela Vierling
angelav@math.bu.edu