물톤 기하
Moulton Geometry
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조회
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다운로드
2
인용
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참고문헌
키워드
초록
물톤 평면은 힐베르트의 평면공리계에서 변-각-변 공리를 제외한 모든 공리가 성립하는 평면으로서 변-각-변 공리의 중요성을 알 수 있게 해 준다. 이 논문은 물톤 평면의 직선, 거리, 각도 등의 정의로부터 시작하여 물톤 평면에서 성립하는 여러 정리들을 소개하고 많은 정리에 대하여 나름대로의 간단한 예를 통한 증명이나 해설, 특히 물톤 원의 접선과 물톤 평면의 강체사상에 대한 독자적 고찰을 제공한다.
Abstract
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.
참고문헌 (15)
- Euclid, "The thirteen books of Euclid’s Elements, Vols. 1,2,3" (1956), Dover Publications
- M. J. Greenberg, "Old and New Results in the Foundations of Elementary Plane Euclidean and Non-Euclidean Geometries", American Mathematical Monthly, 117(3), pp.198~219 (2010)
- M. J. Greenberg, "Euclidean and Non-Euclidean Geometries : Development and History" (1980), W. H. Freeman and Company
- M. Hallett, "David Hilbert’s Lectures on the Foundations of Geometry" (2004), Springer
- Robin Hartshorne, "Geometry: Euclid and beyond, Undergraduate Texts in Mathematics" (2000), Springer-Verlag
- D. Hilbert, "Úber ternáre definite Formen", Mathematische Annalen, pp.169~197 (1893)
- D. Hilbert, "The Foundations of Geometry" (1902), Kessinger Publishing
- D. Hilbert, "The Foundations of Geometry" (1902), The open court publishing company
- D. Hilbert, "The Foundations of Geometry" (1902), The open court publishing company
- D. Hilbert, "Foundations of Geometry" (1971), Open Court
- George E. Martin, "The foundations of geometry and the non-Euclidean plane" (1975), Springer
- Edwin Moise, "Elementary Geometry From an Advanced Standpoint" (1963), Addison Wesley, Reading, MA
- F. R. Moulton, "A simple non-Desarguesian plane geometry", Transactions of the AMS, pp.192~195 (1902)
- H. Poincare, "Poincare’s review of Hilbert’s ‘Foundations of Geometry’", Bulletin of the AMS, pp.1~23 (1903)
- 양성덕, "힐베르트의 저서‘기하학의 기초’에 관하여", 한국수학사학회지, 24(4), pp.61~86 (2011), 한국수학사학회