An article co-authored by Professor of Mathematics Robert Kantrowitz ’82 appears in the July 2019 edition of The Mathematical Gazette.
The paper, titled “Launching a projectile to cover maximal area,” was written with Michael M. Neumann of Mississippi State University. It details various approaches to an optimization problem that arises in connection with modeling the flight of a projectile.
According to the authors, the quantity to be maximized is the area under the trajectory of the projectile, which thus entails the handling of a canonical integral function.
“While natural attempts using Fermat’s theorem from elementary calculus or an ancient result of Archimedes both fail,” they say, “a theorem of Leibniz for differentiation under the integral sign yields a surprisingly simple formula for the angle of launch that provides the greatest possible area.”
Along the way, the Kantrowitz and Neumann confront the limitations of computer algebra systems to assist with the computations that arise in this context.