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Gauss (Schweikart and Taurinus) and Gauss’s Differential Geometry

  • Jeremy Gray
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

In the 1820s the hitherto unthinkable was gradually thought. Friedrich Karl Schweikart, a law professor, wrote to Carl Friedrich Gauss with some further consequences of Saccheri’s and Lambert’s ideas, which Gauss accepted and improved. Schweikart’s nephew, Franz Adolf Taurinus, however, used a lengthy inverstigation as the basis for a fallacious refutation of the new geometry, and Gauss refused to be associated with his work. As for what Gauss knew, the question is complicated: he accepted the possibility of a new geometry but never gave a connected account of it, even when, as briefly discussed here, he had discovered the intrinsic nature of the curvature of a surface.

Keywords

Gaussian Curvature Zero Curvature Constant Positive Curvature Trigonometrical Formula Mysterious Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of MathematicsThe Open UniversityWalton Hall, Milton KeynesUnited Kingdom
  2. 2.The Mathematics InstituteThe University of WarwickWarwickUnited Kingdom

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