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Journal of Geometry

, 110:52 | Cite as

The elementary Archimedean axiom in absolute geometry

  • Victor PambuccianEmail author
Article
  • 54 Downloads

Abstract

Absolute planes in which the elementary Archimedean axiom holds satisfy Aristotle’s axiom. Absolute planes satisfying both the elementary Archimedean axiom and Bachmann’s Lotschnittaxiom are Euclidean. The Corollary to Aristotle’s axiom is equivalent to Aristotle’s axiom.

Keywords

Absolute plane geometry elementary Archimedean axiom Aristotle’s axiom Lotschnittaxiom Euclidean parallel postulate 

Mathematics Subject Classification

Primary 51F05 Secondary 03B30 

Notes

References

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical and Natural Sciences (MC 2352)Arizona State University - West CampusPhoenixUSA

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