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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| Format: | Article |
| Language: | English |
| Published: |
Editura Universităţii "Petru Maior"
2017-12-01
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| Series: | Scientific Bulletin of the ''Petru Maior" University of Tîrgu Mureș |
| Subjects: | |
| Online Access: | http://scientificbulletin.upm.ro/papers/2017-2/7_Remarks%20on%20generalization_FintaB.pdf |
| Summary: | 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 |
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| ISSN: | 1841-9267 2285-438X |