Segment Arithmetic

  • Robin Hartshorne
Part of the Undergraduate Texts in Mathematics book series (UTM)


Segment arithmetic allows us to complete the chain of logical connections between an abstract geometry satisfying axioms studied in Chapter 2 with the geometries over fields studied in Chapter 3. We will show how to define addition and multiplication of line segments in a Hilbert plane satisfying the parallel axiom (P). In this way, the congruence equivalence classes of line segments become the positive elements of an ordered field F (Section 19). Using this field F we can recover the usual theory of similar triangles (Section 20).


Line Segment Positive Element Cartesian Plane Similar Triangle Angle Bisector 
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Copyright information

© Robin Hartshorne 2000

Authors and Affiliations

  • Robin Hartshorne
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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