Area of reduced polygons
Marek Lassak · Publicationes Mathematicae Debrecen · 2005
A convex body R of Euclidean space E d is said to be reduced if every convex body P ⊂ R different from R has thickness smaller than the thickness ∆(R) of R. We prove that the area of every reduced polygon R is smaller than 1 4 π •∆ 2 (R) and that the factor 1 4 π cannot be lessened.We conjecture that the area of every planar reduced body is at most 1 4 π • ∆ 2 (R).