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
What to turn in:
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.
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
Turn in a sketchpad file electronically by emailing it to firstname.lastname@example.org.
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.