Vectors and a half-disk of triangle shapes in Ionescu-Weitzenb\"ock's inequality
Abstract
The aim of this note is to give two new conceptual proofs of Ionescu-Weitzenb\"ock's inequality. The first one, which is a vector proof, provides us a geometric interpretation of the difference between the two sides of this inequality and of two known corollary inequalities in differential geometry. Through a less classical approach, our second proof makes use of the properties of the set of triangles with a fixed "size", seen as a half-disk.
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