“Artifacts of Research: On Singularities” by Chertok

  • ©Jonathan D. Chertok


Entry Number: 05


    Artifacts of Research: On Singularities



    Relatively recent developments in computer visualization have, among other things, focused increasing interest on a classical mathematical model collection originally made by hand in plaster in the 1860’s. Much like the effort to classify the animal kingdom this was an effort to catalog the mathematical universe.

    I welcome the opportunity to exhibit a full-size recreation of the largest series in this collection – the series designed to represent types of singularities possible on a cubic surface. These models were created by Carl Rodenberg for his thesis and produced under the direction of Felix Klein (1849 – 1925) the founder of modern topology. They are recreated here as plaster-based Rapid Prototyping (RP) models. Additionally presented are unique new models of the Clebsch Diagonal Cubic, a so-called “smooth” surface and the “god-head” of the series from which the series of singularities originate.

    I would also like to direct your attention to a video of the Clebsch Diagonal Cubic which simultaneously demonstrates the complex geometric configuration of this famous surface and gives some insight into the Computer-Aided Design (CAD) origins of the work.

    I am currently at work on a comprehensive, illustrated summary of the typology and mathematics behind these forms to accompany the exhibition.


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