The Pizza Tray Is Too Small and Nobody Planned for This

Abstract:  The pizza is too large for the tray. We study how much of a circular pizza of radius R can be retained as one connected piece inside a circular tray of radius r < R using n straight cuts. For a tray-arc span S, we derive an exact area formula and reduce the whole crisis to a one-variable numerical maximization. As n approaches infinity, the retained area approaches the full tray area, although the required knife work approaches a cry for help.