Nonstandard Geometric Proofs

  • Jacques D. Fleuriot
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2061)

Abstract

This paper describes ongoing work in our formal investigation of some of the concepts and properties that arise when infinitesimal notions are introduced in a geometry theory. An algebraic geometry theory is developed in the theorem prover Isabelle using hyperreal vectors. We follow a strictly definitional approach and build our theory of vectors within the nonstandard analysis (NSA) framework developed in Isabelle. We show how this theory can be used to give intuitive, yet rigorous, nonstandard proofs of standard geometric theorems through the use of infinitesimal and infinite geometric quantities.

Keywords

Theorem Prove Signed Area Nonstandard Analysis Automate Deduction Polygonal Area 
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 Berlin Heidelberg 2001

Authors and Affiliations

  • Jacques D. Fleuriot
    • 1
  1. 1.Division of InformaticsUniversity of EdinburghEdinburgh

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