On Polya's Orchard Problem
Alexandru Hening, Michael Kelly · Rose-Hulman Scholar (Rose–Hulman Institute of Technology) · 2006
In 1918 Polya formulated the following problem: ``How thick must the trunks of the trees in a regularly spaced circular orchard grow if they are to block completely the view from the center?" (Polya and Szego [2]). We study a more general orchard model, namely any domain that is compact and convex, and find an expression for the minimal radius of the trees. As examples, solutions for rhombus-shaped and circular orchards are given. Finally, we give some estimates for the minimal radius of the trees if we see the orchard as being 3-dimensional.