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.


Cross Product Signed Area Analytic Geometry Geometric Concept Basic Axiom 
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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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