Optimizing Prisms of All Shapes and Dimensions

Summary

We generalize the standard calculus problem of finding the optimal shape of a square prism to allow bases of any shape and then extend to arbitrary dimension. In all cases, the prism with the smallest possible surface area given the volume has height twice the apothem of the base (where the definition of apothem has been suitably generalized).

Additional information

Notes on contributors

Maria Nogin

Maria Nogin ([email protected]) received her undergraduate degree from Moscow State University in 1998 and her Ph.D. from the University of Rochester in 2003, both in mathematics. Since then, she has been teaching a wide range of courses at the California State University, Fresno, where she is currently an associate professor. Nogin's passion is problem solving, so she is always striving to find and generalize interesting problems in all the courses she is teaching, including calculus. She also loves to camp and hike in the mountains.