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Pythagorean Theorem I: In non-Hilbert Geometry

피타고라스의 정리 I: 비-힐베르트 기하에서

  • Received : 2018.08.23
  • Accepted : 2018.11.10
  • Published : 2018.12.31

Abstract

Pythagorean thoerem exists in several equivalent forms in the Euclidean plane, that is, the Hilbert plane which in addition satisfies the parallel axiom. In this article, we investigate the truthness and mutual relationships of those propositions in various non-Hilbert planes which satisfy the parallel axiom and all the Hilbert axioms except the SAS axiom.

Acknowledgement

Supported by : 목포해양대학교, 한국연구재단

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