On Polya's Orchard Problem

Authors

Alexandru Hening, International University Bremen, GermanyFollow
Michael Kelly, Oklahoma State UniversityFollow

Abstract

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.

Author Bio

Alexandru Hening is a math major at IUB (International University,Bremen, Germany). He is expected to receive his BS degree in May '06. Heintends to pursue a Ph.D. in mathematics and to do research in NumberTheory and Algebraic Geometry.

Michael Kelly is currently an undergraduate math major at Oklahoma State University. He is expected to graduate May '06. The areas of math he is most interested in are topology and algebraic geometry. After graduation he intends to pursue a Ph.D. in mathematics

Faculty Sponsor

Boris Bekker

Recommended Citation

Hening, Alexandru and Kelly, Michael (2006) "On Polya's Orchard Problem," Rose-Hulman Undergraduate Mathematics Journal: Vol. 7: Iss. 2, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss2/9