Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-02-11T19:32:17.663Z Has data issue: false hasContentIssue false
  • English
  • Français

Some generalisations of Weitzenböck’s inequality

Published online by Cambridge University Press:  11 October 2023

Quang Hung Tran
Quang Hung Tran*
Affiliation:
High school for Gifted Students, Hanoi University of Science, Vietnam National University at Hanoi, 182 Luong The Vinh, Thanh Xuan, Hanoi, Vietnam. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

Throughout this Article, we use the following notations for the triangle ABC

  • a, b and c are the lengths of the sides BC, CA and AB, respectively,

  • Δ denotes the area of triangle ABC,

  • ha, hb and hc are the lengths of the altitudes through the vertices A, B and C, respectively,

  • ma, mb and mc are the lengths of the medians through the vertices A, B and C, respectively.

Type
Articles
Information
The Mathematical Gazette , Volume 107 , Issue 570 , November 2023 , pp. 405 - 411
Check for updates
Copyright
© The Authors, 2023 Published by Cambridge University Press on behalf of The Mathematical Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Weitzenböck, R., Über eine Ungleichung in der Dreiecksgeometrie, Math. Zeitschr. 5 (1919) pp. 137–146.CrossRefGoogle Scholar
Pedoe, D., On some geometric inequalities, Math. Gaz. 26 (December 1942) pp. 202–208.CrossRefGoogle Scholar
Alsina, C. and Nelsen, R. B., Geometric Proofs of the Weitzenböck book and Hadwiger-Finsler inequalities, Maths. Mag. 81 (June 2008) pp. 216–219.CrossRefGoogle Scholar
Engel, A., Problem-solving strategies, Springer-Verlag (1998).Google Scholar
Finsler, P., Hadwiger, H., Einige Relationen im Dreieck, Commentarii Mathematici Helvetici, 10 1, (1937) pp. 316–326.CrossRefGoogle Scholar
Lukarevski, M., The circummidarc triangle and the Finsler-Hadwiger inequality, Math. Gaz. 104 (July 2020) pp. 335–338.CrossRefGoogle Scholar
Lukarevski, M., Marinescu, D. S., A refinement of the Kooi’s inequality, Mittenpunkt and applications, J. Inequal. Appl. 13(3), (2019) pp. 827–832.CrossRefGoogle Scholar
Lukarevski, M., A simple proof of Kooi’s inequality, Math. Mag. 93 (3), (2020) p. 225.CrossRefGoogle Scholar
Bogomolny, A., Sides and area of pedal triangle, Interactive mathematics miscellany and puzzles, available at https://www.cut-the-knot.org/triangle/PedalTriangle.shtml Google Scholar
Leversha, G., The geometry of the triangle, UKMT (2013).Google Scholar
Johnson, R. A., Advanced Euclidean Geometry (Modern Geometry), Dover, 1960, pp. 135–141.Google Scholar
Wolfram. MathWorld, Fermat Points accessed March 2023 at https://mathworld.wolfram.com/FermatPoints.html Google Scholar
Kimberling, C., Encyclopedia of triangle centers, X(13) and X(14) at http://faculty.evansville.edu/ck6/encyclopedia/ETC.html Google Scholar
Tran, Q. H. (buratinogigle), Relation with Fermat points, AoPS at https://artofproblemsolving.com/community/g4h1968407 Google Scholar
Kimberling, C., Triangle centers and central triangles, Congr. Numer., (1998) pp. 67–68.Google Scholar
Scott, J. A., Some examples of the use of areal coordinates in triangle geometry, Math. Gaz., 83 (November 1999), pp. 472–477.CrossRefGoogle Scholar