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Abstract

This chapter covers some of the concepts and properties that arise when infinitesimal notions are introduced in the geometry theory. The hyperreal space is shown to have a practical and rich application in geometry. A few theorems and proofs are examined. Also as an important part of this work, some algebraic geometry is developed using hyperreal vectors. This is a definitional approach used to formalize notions from the traditional GTP methods and to verify their basic axioms. We start with a brief review of non-Archimedean geometry.

Keywords

Cross Product Signed Area Analytic Geometry Geometric Concept Basic Axiom 
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 2001

Authors and Affiliations

  • Jacques Fleuriot
    • 1
  1. 1.Division of InformaticsUniversity of EdinburghEdinburghUK

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