December 20, 2007
To the Editors of the Rose-Hulman Undergraduate Math Journal,
It is my pleasure to sponsor Marissa Predmore’s submission to your journal. Her paper
titled The Box Problem is a result of work she did under my supervision as part of her
undergraduate senior thesis here at California Lutheran University. The entirety of her
work was done when she was an undergraduate.
Marissa’s paper answers two questions posed by Phillip Hotchkiss in a 2002 article
published in the College Mathematics Journal. The questions pertain to the dimensions
of a rectangular piece of cardboard that is used to construct a box with an open top by
cutting out a square from each corner and bending up the sides. She shows that the
smallest distinct integer dimensions for obtaining a rational height of the box are 3 and 8.
She also shows that the smallest distinct integer dimensions for obtaining an integral
height of the box are 5 and 8. She then states (and provides evidence for) her own
conjecture on minimizing the second dimension of the box when given the first
dimension.
In my opinion, this is a well-written paper that should be interesting to a wide range of
readers. Marissa’s work was done over the course of two semesters and certainly has a
level of mathematical maturity that is beyond a typical homework assignment.
If I can be of any further assistance, please do not hesitate to contact me. You will find
my contact information at the bottom of this letter.
Sincerely,
Christina L. Soderlund, Ph.D.
Assistant Professor, Department of Mathematics
California Lutheran University
Mathematics Department
60 West Olsen Road #3750
Thousand Oaks, CA 91360
phone: (805) 493-3046
email: csoderlu@callutheran.edu
www.callutheran.edu