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 ). 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.
Boris Bekker, Department of Mathematics, Central Michigan Universitybekke1b@cmich.edu
Hening, Alexandru and Kelly, Michael
"On Polya's Orchard Problem,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 7
, Article 9.
Available at: http://scholar.rose-hulman.edu/rhumj/vol7/iss2/9