On the minimal area of quadrangles circumscribed about planar convex bodies

2025/06/05 by Fodor, Ferenc, Grundbacher, Florian
#52A27 (Primary) 52A10 #52A40 (Secondary) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2506.05185

Abstract

We show that every planar convex body is contained in a quadrangle whose area is less than (1 - 2.6 ⋅ 10^-7) √(2) times the area of the original convex body, improving the best known upper bound by W. Kuperberg.

Related

• A convex cover for closed unit curves has area at least 0.0975
• Area bounds for planar convex bodies containing a fixed number of interior integral points
• A convex cover for closed unit curves has area at least 0.1
• A note on the convex body isoperimetric conjecture in the plane
• Optimal Area-Sensitive Bounds for Polytope Approximation