Far East Journal of Mathematical Education

The Far East Journal of Mathematical Education is a peer-reviewed journal focused on mathematical education. It publishes research papers that enhance understanding of mathematical concepts and encourages the use of technology, statistics, algorithms, and simulations in mathematics learning.

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PROOF WITHOUT WORDS: A GENERALIZATION OF IONESCU-WEITZENBÖCK’S INEQUALITY

Authors

  • Martin Celli

Keywords:

Ionescu-Weitzenböck's inequality, Hadwiger-Finsler's inequality, cosine law, triangle geometry, proof without words

DOI:

https://doi.org/10.17654/0973563125011

Abstract

We wordlessly prove a generalization of Ionescu-Weitzenböck’s inequality.

Received: March 2, 2025
Accepted: May 16, 2025

References

C. Alsina and R. B. Nelsen, Geometric proofs of the Weitzenbock and Hadwiger-Finsler inequalities, Math. Mag. 81(3) (2008), 216-219.

https://doi.org/10.1080/0025570X.2008.11953553.

D. M. Batinetu-Giurgiu, M. Bencze and D. Sitaru, About Finsler-Hadwiger’s inequality, Rom. Math. Mag. (2021).

http://www.ssmrmh.ro/wp-content/uploads/2021/06/ABOUT-FINSLER-HADWIGERS-INEQUALITY.pdf.

D. M. Batinetu-Giurgiu and N. Stanciu, Some generalizations of Ionescu- Weitzenbock’s inequality, J. Sci. Arts 22(1) (2013), 27-32.

http://josa.ro/docs/josa_2013_1/a_03_Batinetu_Giurgiu_Stanciu_1.pdf.

M. Celli, Vectors and a half-disk of triangle shapes in Ionescu-Weitzenbock’s inequality, Balk. J. Geom. Appl. 24(2) (2019), 1-5.

https://www.emis.de/journals/BJGA/v24n2/B24-2ce-ZG46.pdf.

M. Celli, A generalization of Ionescu-Weitzenbock’s inequality, using Huygens-Steiner’s theorem from mechanics, Glob. J. Adv. Res. Class. Mod. Geom. 13(1) (2024), 116-118.

https://geometry-math-journal.ro/pdf/Volume13-Issue1/11.pdf.

N. G. Heo, A new proof of the Ionescu-Weitzenbock inequality, Math. Mag. 94(2) (2021), 135-136. https://doi.org/10.1080/0025570X.2021.1869494.

E. Stoica, N. Minculete and C. Barbu, New aspects of Ionescu-Weitzenbock’s inequality, Balk. J. Geom. Appl. 21(2) (2016), 95-101.

https://www.emis.de/journals/BJGA/v21n2/B21-2st-b21.pdf.

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Published

06-06-2025

Issue

Vol. 27 No. 2 (2025)

Section

Articles

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How to Cite

PROOF WITHOUT WORDS: A GENERALIZATION OF IONESCU-WEITZENBÖCK’S INEQUALITY. (2025). Far East Journal of Mathematical Education, 27(2), 93-95. https://doi.org/10.17654/0973563125011

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