논문KCI 등재
Generalized Varignon's and medial triangle theorems
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper, we extend the medial triangle theorem and Varignon's theorem to generic two-dimensional polygons and highlight the role played by diagonals in this process. One of the results is a synthetic definition of the concept of median for an $n$-sided polygon.
Abstract
In this paper, we extend the medial triangle theorem and Varignon's theorem to generic two-dimensional polygons and highlight the role played by diagonals in this process. One of the results is a synthetic definition of the concept of median for an $n$-sided polygon.
참고문헌 (17)
- H. S. M. Coxeter, "Introduction to Geometry" (1961), John Wiley & Sons, Inc
- H. S. M. Coxeter, "Geometry revisited, New Mathematical Library, 19" (1967), Random House, Inc.
- A. Emch, "On the medians of a closed convex polygon", Amer. J. Math, 37(1), pp.19~28 (1915)[DOI]
- Euclid, "Euclid’s Elements of Geometry, Edited and provided with a modern English translation by Richard Fitzpatrick", ~ (2007)
- R. A. Johnson, "Advanced Euclidean geometry: An elementary treatise on the geometry of the triangle and the circle" (1960), Dover Publications, Inc
- B. Khorshidi, "A new method for finding the center of gravity of polygons", J. Geom, 96(1-2), pp.81~91 (2009)[DOI]
- 김동수, "Centroids and some characterizations of parallelograms", 대한수학회논문집, 31(3), pp.637~645 (2016), 대한수학회
- R. B. Kirchner, "Classroom notes : A generalization of the median theorem for triangles", Amer. Math. Monthly, 69(7), pp.650~ (1962)[DOI]
- N. Lord, "92.22 Maths bite: averaging polygons", Math. Gaz, 92(523), pp.134~ (2008)
- M. F. Mammana, "On the centroids of polygons and polyhedra", Forum Geom, 8, pp.121~130 (2008)
- E. E. Moise, "Elementary Geometry from an Advanced Standpoint" (1990), Addison-Wesley Publishing Company
- P. N. Oliver, "Consequences of the Varignon parallelogram theorem", The Mathematics Teacher, 94(5), pp.406~408 (2001)
- A. Ostermann, "Geometry by Its History" (2012), Springer
- A. Palatnik, "Proof without words : Varignon’s theorem", College Math. J, 48(5), pp.354~ (2017)[DOI]
- G. C. Shephard, "Centroids of polygons and polyhedra", Math. Gaz, 74(467), pp.42~43 (1990)
- J. Stillwell, "The Four Pillars of Geometry" (2005), Springer
- P. Varignon, "Elemens de Mathematique de Monsieur Varignon", Springer
관련 논문AI추천
Centroids and some characterizations of parallelograms김동수, 윤대원, Jeong Ki Yang, Kwang Seuk Lee, Kyung Bum Lee, Seongjin Son, Yoon Il Lee대한수학회 · 대한수학회논문집2016 · 제31권 제3호Various centroids of polygons and some characterizations of rhombi김동수, 김원용, 윤대원, 이광석대한수학회 · 대한수학회논문집2017 · 제32권 제1호Pascal's hexagon theorem reproved by elementary tools only최인송대한수학회 · 대한수학회논문집2022 · 제37권 제4호Area of triangles associated with a curve II김동수, 김영호, Dae Heui Park, Wonyong Kim대한수학회 · 대한수학회보2015 · 제52권 제1호Some characterizations of conics and hypersurfaces with centrally symmetric hyperplane sections김동서, 김동수, 김원용, 방신옥대한수학회 · 대한수학회논문집2024 · 제39권 제1호Area of triangles associated with a curve김동수, 심규철대한수학회 · 대한수학회보2014 · 제51권 제3호
이 간행물의 다른 논문 (23건)
Estimates for certain shifted convolution sums involving Hecke eigenvaluesGuodong Huapp. 319-330MAXIMAL CHAIN OF IDEALS AND n-MAXIMAL IDEALHemin A. Ahmad, Parween A. Hummadipp. 331-340Simple formulations on circulant matrices with alternating FibonacciSugi Guritmanpp. 341-354Unitary analogues of a generalized number-theoretic sumTraiwat Intarawong, Boonrod Yuttananpp. 355-364On graded $J$-ideals over graded ringsTamem Al-Shorman, Ece Yetkin Celikel, Malik Batainehpp. 365-376
