Английская Википедия:Bonnesen's inequality

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Шаблон:Short description Bonnesen's inequality is an inequality relating the length, the area, the radius of the incircle and the radius of the circumcircle of a Jordan curve. It is a strengthening of the classical isoperimetric inequality.

More precisely, consider a planar simple closed curve of length <math>L</math> bounding a domain of area <math>A</math>. Let <math>r</math> and <math>R</math> denote the radii of the incircle and the circumcircle. Bonnesen proved the inequality <math display=block> \pi^2 (R-r)^2 \leq L^2-4\pi A. </math>

The term <math> L^2-4\pi A</math> in the right hand side is known as the isoperimetric defect.

Loewner's torus inequality with isosystolic defect is a systolic analogue of Bonnesen's inequality.

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Шаблон:Geometry-stub