Article overview
Abstract
We give three new proofs of the triangle inequality in Euclidean Geometry. There seems to be only one known proof at the moment. It is due to properties of triangles, but our proofs are due to circles or ellipses. We aim to prove the triangle inequality as simple as possible without using properties of triangles. In other words, we suggest proofs without using paper and pen.
Keywords and Phrases
Triangle inequalitycircleellipsefocci of ellipseEuclidean geometryalgebraic geometry.
AMS Subject Classification
26D05, 26D15, 51M16.
Reference information
How to Cite
Norihiro Someyama, Mark Lyndon Adamas Borongan (2019). NEW PROOFS OF TRIANGLE INEQUALITIES. Journal of Ramanujan Society of Mathematics and Mathematical Sciences, 7(1), 85-92.