Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s). Each week’s entries are scored by a panel of faculty judges, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button. The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.
The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited! Send solutions to firstname.lastname@example.org or put solutions in the marked envelope in the hallway outside Glatfelter 215. This problem was posted on Friday, February 15 and solutions are due on Friday, February 22 by 5:00 p.m.
There are a lot of circles that we could draw that lie entirely in the region between the x-axis and the part of the parabola y = 1-x^2 that lies above the x-axis.
Find the largest possible area of such a circle. Make it clear that your proposed circle really does lie in the region described (touching the edge is OK!), and explain how you know that the area is largest possible.