A New Take on Classic ‘Pen Problems’

AbstractIn this article we generalize the classic “farm pen” optimization problem from a first course in calculus in a handful of different ways. We describe the solution to an n-dimensional rectangular variant, and then study the situation when the pens are either regular polygons or platonic solids. Additional informationNotes on contributorsDavid A. Nash David A. Nash (prof.nash@gmail.com) is a data scientist at the consulting firm Kin + Carta. After an undergraduate career at Santa Clara University, he earned his Ph.D. from University of Oregon in 2010 with an emphasis in representation theory. From 2010 to 2021, he served as an associate professor of mathematics at Le Moyne College. He enjoys sharing his passion for mathematics and problem solving with students, colleagues, and his children.