线 ,
, 和
是三角形中线
,
, 和
的等角共轭线,被称为三角形的西梅迪安。西梅迪安线共点于一点
,该点称为西梅迪安点,它是三角形重心
的等角共轭点。
西梅迪安
参见
等角共轭, 西梅迪安点, 西梅迪安三角形, 三角形重心, 三角形中线使用 Wolfram|Alpha 探索
参考文献
Casey, J. "Theory of Isogonal and Isotomic Points, and of Antiparallel and Symmedian Lines." Supp. Ch. §1 in A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., pp. 165-173, 1888.Coolidge, J. L. A Treatise on the Geometry of the Circle and Sphere. New York: Chelsea, p. 65, 1971.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 213-218, 1929.Lachlan, R. An Elementary Treatise on Modern Pure Geometry. London: Macmillian, pp. 62-63, 1893.Mackay, J. S. "Symmedians of a Triangle and Their Concomitant Circles." Proc. Edinburgh Math. Soc. 14, 37-103, 1896.在 Wolfram|Alpha 中被引用
西梅迪安请引用为
Weisstein, Eric W. "Symmedian." 来自 MathWorld--Wolfram 网络资源。 https://mathworld.net.cn/Symmedian.html