The Blaschke-Steinhardt point of a planar convex set (Q1339815)

Let \(K\) be a convex body in Euclidean plane and let \(x\) be an interior point of \(K\). The symbol \((K^*;x)\) denotes the polar body of \(K\) with respect to \(x\) as the point of the polarity, i.e. as the center of the unit circle in respect to which the polarity is defined. The author considers the problem of finding a polarity point \(x\) for which the perimeter \(L(K^*;x)\) of \((K^*;x)\) is minimal. He presents a computational algorithm finding a point of polarity for which the function \(L(P^*;x)\), where \(P\) is an arbitrary convex polygon, attains a local minimum.