Some applications of signed distances in triangles and circles
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry - Tập 64 - Trang 877-886 - 2022
Tóm tắt
We present generalizations of Carnot’s theorem and of the classical Erdös–Mordell inequality.
Tài liệu tham khảo
Bankoff, L.: An elementary proof of the Erdös–Mordell theorem. Amer. Math. Mon. 65(7), 521 (1958)
Coxeter, H.S.M.: Some applications of trilinear coordinates. Linear Algebra Appl. 226–228, 335–388 (1995)
Coxeter, H.S.M.: Introduction to geometry. Wiley, NewYork, 716-721 (1969)
Dao, O.T., Nguyen, D.T., Pham, M.N.: A strengthened version of the Erdös–Mordell inequality. Forum Geom. 16, 317–321 (2016)
Dergiades, N.: Signed distances and the Erdös–Mordell Inequality. Forum Geom. 4, 67–68 (2004)
Ghandehari, M., Martini, H.: On the Erdös–Mordell inequality for normed planes and spaces. Studia Sci. Math. Hungar. 55(2), 174–189 (2018)
Klain, D.A.: The Minkowski problem for polytopes. Adv. Math. 185, 270–288 (2004)
Lang, S.: Introduction to Linear Algebra, 3rd edn. Springer, New York (1987)
Richeson, D.: The Japanese Theorem for Nonconvex Polygons. Loci: Convergence vol 4 (2013), available at https://www.maa.org/press/periodicals/loci/the-japanese-theorem-for-nonconvex-polygons
Tran, Q.H.: A family of weighted Erdös–Mordell inequality and applications. J. Geom. 112(3), Paper No. 33 (2021)