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Miklos Schweitzer 1980_9

Source: divide by straight lines a quadrangle of unit area

January 28, 2009
geometryperimeteradvanced fieldsadvanced fields unsolved

Problem Statement

Let us divide by straight lines a quadrangle of unit area into n n subpolygons and draw a circle into each subpolygon. Show that the sum of the perimeters of the circles is at most πn \pi \sqrt{n} (the lines are not allowed to cut the interior of a subpolygon). G. and L. Fejes-Toth
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