A New Look at the Fundamental Triangle Inequality. Issue 2 (15th March 2023)

• Record Type: Journal Article
• Authors: Lukarevski, Martin
• Is Part Of: Mathematics magazine. Volume 96:Issue 2(2023)
• Page Start: 141
• Page End: 149
• Publication Date: 2023-03-15
• Subjects: 51M16; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/0025570X.2023.2176106
• Languages: English
• ISSNs: 0025-570X

Abstract

Summary: We give a simple proof of the fundamental inequality of the triangle based on calculation of the cosine of an angle in one particular triangle formed from familiar centers. For the term R ( R − 2 r ) which appears in the inequality we give a bound as a rational expression in terms of R and r . Then as an application we derive new refinements of Gerretsen's and Kooi's inequalities.