DOI QR코드

DOI QR Code

물톤 기하

Moulton Geometry

  • 투고 : 2016.01.21
  • 심사 : 2016.06.20
  • 발행 : 2016.06.30

초록

Moulton plane is the plane where all the plane axioms of Hilbert except the side-angle-side axiom hold true, and enables us to understand the importance and significance of the side-angle-side axiom. In this article, we start with the definitions of the Moulton lines, distance, angle, and then introduce many theorems of the Moulton geometry, with many intuitive proofs or explanations of our own with appropriate examples. In particular, we provide our independent study of the tangent lines to the Moulton circles and the rigid motions of the Moulton plane.

키워드

참고문헌

  1. EUCLID, The thirteen books of Euclid's Elements, Translated with introduction and commentary by Sir Thomas L. Heath, Vols. 1,2,3, Dover Publications, Inc., New York, 1956.
  2. M. J. GREENBERG, Old and New Results in the Foundations of Elementary Plane Euclidean and Non-Euclidean Geometries, American Mathematical Monthly 117(3) (March 2010), 198-219. https://doi.org/10.4169/000298910x480063
  3. M. J. GREENBERG, Euclidean and Non-Euclidean Geometries : Development and History, W. H. Freeman and Company, San Francisco, 1980.
  4. M. HALLETT, U. MAJER, eds., David Hilbert's Lectures on the Foundations of Geometry, Springer, New York, 2004.
  5. Robin HARTSHORNE, Geometry: Euclid and beyond, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 2000.
  6. D. HILBERT, Uber ternare definite Formen, Mathematische Annalen 17 (1893), 169-197.
  7. D. HILBERT, The Foundations of Geometry, 1st ed, Authorized translation by E. J. Townsend, The open court publishing company, 1902. - Kessinger Publishing's Rare Reprints.
  8. D. HILBERT, The Foundations of Geometry, 1st ed, Authorized translation by E. J. Townsend, The open court publishing company, 1902. - BiblioBazaar Reproduction Series.
  9. D. HILBERT, The Foundations of Geometry, 1st ed, Authorized translation by E. J. Townsend, The open court publishing company, 1902. - LateX Source From Internet.
  10. D. HILBERT, Foundations of Geometry, Translated by Leo Unger from the tenth German Edition, Open Court Classics, Revised and Enlarged by Paul Bernays, Open Court, 1971.
  11. George E. MARTIN, The foundations of geometry and the non-Euclidean plane, Springer, New York, 1975.
  12. Edwin MOISE, Elementary Geometry From an Advanced Standpoint, Addison Wesley, Reading, MA, 1963.
  13. F. R. MOULTON, A simple non-Desarguesian plane geometry, Transactions of the AMS, April, 1902, 192-195.
  14. H. POINCARE, Poincare's review of Hilbert's 'Foundations of Geometry', Bulletin of the AMS, Oct., 1903, 1-23.
  15. YANG Seong-Deog and Jo Kyeonghee, On Hilbert's 'Grundlagen der Geometrie', The Korean Journal of for History of Mathematics 24(4) (2011), 61-68. 양성덕, 조경희, 힐베르트의 저서 '기하학의 기초' 에 관하여, 한국수학사학회지 24권 4호, 2011년 11월, 61-86.