On the fundamental triangle inequality and Gerretsen's double inequality

DOI10.1007/s00022-022-00630-wzbMath1487.51014OpenAlexW4214601855MaRDI QIDQ2116830

Jian Liu

Publication date: 18 March 2022

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-022-00630-w

zbMATH Keywords

Euler inequalityfundamental triangle inequalityGerretsen double inequality

Mathematics Subject Classification ID

Inequalities and extremum problems in real or complex geometry (51M16)

Cites Work

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• A refinement of an equivalent form of a Gerretsen inequality
• Infinitely many Gerretsen-Blundon style quadratic inequalities, all strongest in Blundon's sense
• Further generalization of Walker's inequality in acute triangles and its applications
• Geometric interpretation of Blundon's inequality and Ciamberlini's inequality
• On best quadratic triangle inequalities
• Inequalities concerning the inradius and circumradius of a triangle
• A geometric inequality with applications
• A geometric proof of Blundon's inequalities
• The geometric proof to a sharp version of Blundon's inequalities
• A sharpened version of the fundamental triangle inequality
• General power inequalities between the sides and the circumscribed and inscribed radii related to the fundamental triangle inequality
• Refined geometric inequalities between two or more triangles obtained by dedublation
• Inequalities Associated with the Triangle

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