Theoretical Mathematics and Pedagogical Mathematics (한국수학교육학회지시리즈B:이론수학과 교직수학)

Korean Society of Mathematical Education (한국수학교육학회)
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EULER'S LINE SEGMENT THEORY IN LORENTZIAN AND ISOTROPIC PLANE

  • Jin Ju Seo (Department of Mathematics, Korea University)
  • Received : 2024.09.20
  • Accepted : 2025.01.15
  • Published : 2025.02.28
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Abstract

We examine the length theory of line segments in the Lorentzian plane and the isotropic plane, with emphases the definition of distance.

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Acknowledgement

This thesis is based on the lectures of Professor Seong-Deog Yang from the Department of Mathematics at Korea University. I sincerely hope that this thesis serves as a modest way to repay Professor Yang's guidance.

References

  1. H. S. White: The Geometry of Leonhard Euler. Elsevier B. V. 5 (2007), 303-321. https://doi.org/10.1016/S0928-2017(07)80017-X
  2. Kyung Mi Lee: Elementary Geometry of Circles and Triangles in the Lorentzian Plane. Master's Thesis. Korea University (2011).
  3. Jin Ju Seo: On the quadratic curves in the Lorentz plane. Master's Thesis. Korea University (2011). https://library.korea.ac.kr/detail/?cid=CAT000045289365&ctype=t
  4. Jin Ju Seo: On the geometry of curves and surfaces in the isotropic three-space. Ph.D. Thesis. Korea University (2020). http://www.riss.kr/link?id=T15642008&outLink=K
  5. Jin Ju Seo & Seong-Deog Yang: Zero mean curvature surfaces in isotropic three-space, Bull. Korean Math. Soc. 58 (2021), 1-20. https://doi.org/10.4134/BKMS.b190783
  6. Jin Ju Seo & Seong-Deog Yang: Constant ratio curves in the isotropic plane and their deflection properties, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 28 (2021), 71-89. https://doi.org/10.7468/JKSMEB.2021.28.1.71
  7. I. M. Yaglom: A Simple Non-Euclidean Geometry and Its Physical Basis. Springer Verlag. New York (1979). https://doi.org/10.1007/978-1-4612-6135-3
  8. Seong-Deog Yang: Lecture notes on Differential Geometry 1 (Unpublished). Korea University (2019.5.21).
  9. Seong-Deog Yang: Lecture notes on Elementary Lorentzian geometry (Unpublished). Korea University (2014.8.2).