REMARKS ON A GENERALIZATION OF A QUESTION RAISED BY PÁL ERDOS CONCERNING A GEOMETRIC INEQUALITY IN ˝ ACUTE TRIANGLES

REMARKS ON A GENERALIZATION OF A QUESTION RAISED BY PÁL ERDOS CONCERNING A GEOMETRIC INEQUALITY IN ˝ ACUTE TRIANGLES

The purpose of this paper is to give a negative answer to a possible generalization of an open question raised by Pál Erd˝os, concerning an inequality in acute triangles. We prove here that from a < b < c does not follow a 2k + l 2k a < b2k + l 2k b < c2k + l 2k c in every acu...

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Main Author: Béla FINTA
Format: Article
Language:English
Published: Editura Universităţii "Petru Maior" 2017-12-01
Series:Scientific Bulletin of the ''Petru Maior" University of Tîrgu Mureș
Subjects:
geometrical inequalities
acute triangle
Online Access:http://scientificbulletin.upm.ro/papers/2017-2/7_Remarks%20on%20generalization_FintaB.pdf
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spelling doaj-02c61758a8a547e682c72fcc3814b09a2020-11-25T01:14:44ZengEditura Universităţii "Petru Maior"Scientific Bulletin of the ''Petru Maior" University of Tîrgu Mureș1841-92672285-438X2017-12-01 14 (XXXI)23335REMARKS ON A GENERALIZATION OF A QUESTION RAISED BY PÁL ERDOS CONCERNING A GEOMETRIC INEQUALITY IN ˝ ACUTE TRIANGLESBéla FINTA0“Petru Maior” University of Tîrgu Mure¸sThe purpose of this paper is to give a negative answer to a possible generalization of an open question raised by Pál Erd˝os, concerning an inequality in acute triangles. We prove here that from a < b < c does not follow a 2k + l 2k a < b2k + l 2k b < c2k + l 2k c in every acute triangle ABC, nor the opposite chain of inequalities, where k ∈ N, k ≥ 2, and a, b, c denotes the length of the triangles sites , while la, lb, lc denotes the length of the interior angle bisectors, as usual. We achieve this by constructing effectively two counterexamples, one for each type of inequalitieshttp://scientificbulletin.upm.ro/papers/2017-2/7_Remarks%20on%20generalization_FintaB.pdfgeometrical inequalitiesacute triangle
collection DOAJ
language English
format Article
sources DOAJ
author Béla FINTA
spellingShingle Béla FINTA
REMARKS ON A GENERALIZATION OF A QUESTION RAISED BY PÁL ERDOS CONCERNING A GEOMETRIC INEQUALITY IN ˝ ACUTE TRIANGLES
Scientific Bulletin of the ''Petru Maior" University of Tîrgu Mureș
geometrical inequalities
acute triangle
author_facet Béla FINTA
author_sort Béla FINTA
title REMARKS ON A GENERALIZATION OF A QUESTION RAISED BY PÁL ERDOS CONCERNING A GEOMETRIC INEQUALITY IN ˝ ACUTE TRIANGLES
title_short REMARKS ON A GENERALIZATION OF A QUESTION RAISED BY PÁL ERDOS CONCERNING A GEOMETRIC INEQUALITY IN ˝ ACUTE TRIANGLES
title_full REMARKS ON A GENERALIZATION OF A QUESTION RAISED BY PÁL ERDOS CONCERNING A GEOMETRIC INEQUALITY IN ˝ ACUTE TRIANGLES
title_fullStr REMARKS ON A GENERALIZATION OF A QUESTION RAISED BY PÁL ERDOS CONCERNING A GEOMETRIC INEQUALITY IN ˝ ACUTE TRIANGLES
title_full_unstemmed REMARKS ON A GENERALIZATION OF A QUESTION RAISED BY PÁL ERDOS CONCERNING A GEOMETRIC INEQUALITY IN ˝ ACUTE TRIANGLES
title_sort remarks on a generalization of a question raised by pál erdos concerning a geometric inequality in ˝ acute triangles
publisher Editura Universităţii "Petru Maior"
series Scientific Bulletin of the ''Petru Maior" University of Tîrgu Mureș
issn 1841-9267
2285-438X
publishDate 2017-12-01
description The purpose of this paper is to give a negative answer to a possible generalization of an open question raised by Pál Erd˝os, concerning an inequality in acute triangles. We prove here that from a < b < c does not follow a 2k + l 2k a < b2k + l 2k b < c2k + l 2k c in every acute triangle ABC, nor the opposite chain of inequalities, where k ∈ N, k ≥ 2, and a, b, c denotes the length of the triangles sites , while la, lb, lc denotes the length of the interior angle bisectors, as usual. We achieve this by constructing effectively two counterexamples, one for each type of inequalities
topic geometrical inequalities
acute triangle
url http://scientificbulletin.upm.ro/papers/2017-2/7_Remarks%20on%20generalization_FintaB.pdf
work_keys_str_mv AT belafinta remarksonageneralizationofaquestionraisedbypalerdosconcerningageometricinequalityinacutetriangles
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