As you do this lab, use

1. the Free-Hand Toolbar (on the left) for arbitrary geometric objects (the 'givens' of an elementary folding move) and

2. the Construct and Transform menus for folds that depend on the arbitrary objects

3. Sketchpad methods, rather than folding methods, if they are more convenient

4. menus other than the Measurement menu

5. steps, each of which is justifiable by one of the postulates of Euclidean geometry

Sketchpad Does the Elementary Folding Moves (EFM's):

For each of the following, you should be guided by what you fold on a square sheet of paper, but it's easier to just imagine the Sketchpad sketch plane as a blank sheet of paper on which to represent the folds, and not bother constructing the square itself. (This applies to problem #6, too.)

You will be creating a script for a Sketchpad version of a paper fold. The given objects of the script should correspond to the given objects of the EFM, and the fold should be what is constructed by the script.

If you think any of these are impossible in Sketchpad, explain your thinking.

1. Consider the resulting crease in elementary fold #1 in EFM's. Think about what is given, and what the result is. Then, using Sketchpad, construct the result of this "Line onto Line" fold. Show both the construction process and the resulting fold line of the construction. Print your sketch, make a script, and save your script.

2. Consider the resulting crease in elementary fold #2 in EFM's. Think about what is given, and what the result is. Then, using Sketchpad, construct the result of this "Join Points" fold. Show both the construction process and the resulting fold line of the construction. Print your sketch, make a script, and save your script.

3. Consider the resulting crease in elementary fold #3 in EFM's. Think about what is given, and what the result is. Then, using Sketchpad, construct the result of this "Point onto Point" fold. (It will probably help to consider two separate cases.) Show both the construction process and the resulting fold line of the construction. Print your sketch, make a script, and save your script.

4. Consider the resulting crease in elementary fold #4 in EFM's. Think about what is given, and what the result is. Then, using Sketchpad, construct the result of this "Line onto Itself & through Point" fold. Show both the construction process and the resulting fold line of the construction. Print your sketch, make a script, and save your script.

5. Use patty paper to do elementary fold #5 in EFM's. Think about what is given, and what the result is. Then, using Sketchpad, construct the result of this "Point onto Line & through Point" fold. Show both the construction process and the resulting fold line of the construction. Print your sketch, make a script, and save your script.

Constructing the Folding of a Tangent Envelope:

6. Use patty paper to fold the tangent envelope shown in class. There are instructions and illustrations HERE. Using Sketchpad, construct the collection of repeated folds that form the envelope. Show both the construction process and the locus or trace that results from the the construction. Print your sketch, make a script, and save your script.