Beniamin Bogosel
Abstract
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Gradients of the perimeter and area of a polygon have straightforward geometric interpretations. The use of optimality conditions for constrained problems and basic ideas in triangle geometry show that polygons with prescribed area minimizing the perimeter must be regular.
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Gradients of the perimeter and area of a polygon have straightforward geometric interpretations. The use of optimality conditions for constrained problems and basic ideas in triangle geometry show that polygons with prescribed area minimizing the perimeter must be regular.
Key concepts: Isoperimetric inequality, Perimeter, Polygon (computer graphics), Mathematics, Regular polygon, Isoperimetric dimension, Inequality, Point in polygon