What is Geometry? Is it True? Why is it Important?

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


We look briefly at truth versus proof in geometry, at the controversy between Gottlob Frege and Hilbert, and at the idea of a relative consistency proof.

Extract: Poincaré on the relative consistency of Euclidean and non-Euclidean geometry.


Euclidean Geometry Projective Geometry Axiom System Relative Consistency Pure Logic 


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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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