Moving a Couch around a Corner
This Demonstration illustrates the longest couch that can be placed in a hallway with an L-shaped corner for a given set of hallway widths, a couch width, and an angle. As the angle changes, the displayed couch extends so that it always touches the hallway walls and the inside corner. The longest couch which can make it around the corner is the shortest of these extendable couches. A graph displays the current couch length compared to all couch lengths, and a checkbox adds the longest couch that can make it around the corner to both the diagram and the graph.
C. Moretti, "Moving a Couch around a Corner," The College Mathematics Journal, 33(3), 2002 pp. 196–200.