When the top left corner of a piece of paper is folded down to touch the bottom edge of the paper, a triangle is formed in the lower left corner, as shown below. Model this situation in Sketchpad. Now use the sketch to answer the following question: When is the lower-left triangle as big as possible?
 

Further challenges:
 

1. Can you prove that your answer is correct?  It may be helpful to recall that you probably learned about maximization problems in a calculus class.
2. Your sketch probably falls apart when the point is dragged too close to the lower-right corner. Extend your sketch to show (and smoothly transition into) this third possible state. Can you construct a sketch in which the corner point can be dragged all the way around the edge of the piece of paper?

• Turn in a sketchpad file electronically by emailing it to nat@alumni.princeton.edu.  See how pretty you can make it!  The file you submit should be named by your last name.
• Also turn in a written explaination of when the triangle is as big as possible, and your proof that you're right.