Home > RHUMJ > Vol. 7 (2006) > Iss. 2

#### Article Title

#### 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.

#### Sponsor

Boris Bekker, Department of Mathematics, Central Michigan Universitybekke1b@cmich.edu

#### 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:
http://scholar.rose-hulman.edu/rhumj/vol7/iss2/9