The Open Box Problem

Here's a virtual maniupulative for constructing an open box from a rectangle. You can learn more by downloading my presentation on the "Inverse of the Open Box Problem." (MAA Rocky Mountain Regional Meeting, 2007)

Using the Box Applet

  • Click and Drag the Black Points to change the box.
  • Click and Drag elsewhere to rotate the whole image.
  • Hold down Shift and Click/Drag to Zoom in and out.
  • Press the Home button on your keyboard to restore the original image.

Some questions you might want to consider:

  • For the 33 by 40 rectangle, what cutaway number, x, produces the box with maximum volume? Can you explain why?
  • If you change the dimensions of the rectangle, how does the optimal cutaway number change?
  • What is the "trick" for finding the ideal cutaway number for a square?