# Off on a Tangent 18.06

### Problem solvers of the fortnight

Congratulations to Pablo Bejarano, Josiah Brett, Griffin Bruso, Anna Carlson, Luke Christensen, Austin Cortes, Adair Cutler, Liz Cutlip, Adam Czeranko, Eli Edwards-Parker, Liam Faber, Mackenzie Green, Blake Harlow, Jacob Harrelson, Rebekah Harrelson, Adam Heisler, Fiona Johnson, Tyler Koran, Jacob Kowalski, Peter Le, Rebekah Ludema, James Mandeville, Matthew Nguyen, Josie Surel, Hugh Thiel, Karsten VanFossen, Bethany VanHouten, Nolan Vandegrift, Joseph Weber, Tracy Westra, Kamaron Wilcox, and William Zywicki — all of whom correctly solved the problem in the last issue of our fortnightly rag.

### Problem of the fortnight

A circular disk of radius r < 1 rolls along the interior of a 1 × 1 square, always tangent to at least one of the sides.  (The picture below shows two sample locations of the circle.) What value of r maximizes the total area covered by the disk, and what is the total area the circle sweeps out as it rolls along the interior of the square?

Write your solution on a square of paper, and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson’s office, room 212 in The Werf, by 3:00 p.m. on Friday, December 6.  As always, be sure to include your name and the name(s) of your math professor(s) — for example, Ray D. Oss, Professors C. Cant and Cy Kloyd — on your solution.  Good luck and have fun!