Two identical squares can be made to overlap in many ways. Here are two such methods.[br][br]Varying the overlap slider varies the degree of overlap. In the right hand panel the[br]area in common for each method is plotted as a function of the degree of overlap.[br][br]Which function corresponds to which method? How do you know?[br][br]Why is one function linear and the other not?[br][br]What is the non-linear function? How do you know?[br][br]What conjectures do you have about the nature of the common area function for [br]convex polygons other than squares?[br][br]What conjectures do you have about the common area function if the two squares[br]are not related by a simple translation along a line of symmetry?[br][color=#ff0000][i][b][br]What questions could/would you ask your students based on this applet?[/b][/i][/color]