Some extremal problems for polygons in the Euclidean plane
Yu.G. Nikonorov, O.Yu. Nikonorova
TL;DR
This paper investigates extremal problems concerning convex polygons in the Euclidean plane, focusing on perimeter-related questions, presenting simple formulations with complex proofs, and discussing open related problems.
Contribution
It provides new results on extremal perimeter problems for convex polygons and discusses related open problems, with a focus on simple formulations and intricate proofs.
Findings
New extremal perimeter bounds for convex polygons
Identification of open problems in polygon extremal theory
Complex proofs for simple formulations of perimeter problems
Abstract
The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane and their perimeters. We present a number of results that have simple formulations, but rather intricate proofs. Related and still unsolved problems are discussed too.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Point processes and geometric inequalities · Mathematics and Applications