Math 342
Modern Geometry II
Computer Lab I: Paper Folding



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?
What to turn in: