The objective of this lab is to come up with a collection of what might be called Elementary Folding Moves (EFM's) to describe all the possible single folds anyone could ever need - to do whatever folding project she might want to complete. Not to be too ambitious, however, the collection should only include two-dimensional moves that involve folding one layer of paper flat onto another layer and creasing. WHY THIS LAB IS HARD

The collection should have the following properties:

1. Each EFM should be a single fold, making a single line (crease).

2. The collection should include all folds one could ever want or need.

3. Each EFM should be described simply and unambiguously, referring only to points and lines (creases) that are already on the paper.

4. No EFM should depend on a specific context. Only the given objects (points and lines) should be used in the description. You may label points and lines (like P, Q, R, L, M, N, etc.) but you must avoid such contextual specifics as "corner of the paper" and "lower edge." (However, when the EFM is applied, the context will be used.)

5. The consequences (properties of the resulting fold in relation to what is given) of each EFM should be included. For example, what has been called the Fundamental Folding Property (about the consequence of folding a perpendicular bisector) is a consequence of a certain elementary fold.

Stage 1

To start the process of writing the collection of EFM's, form five groups, with each group generating EFM's needed to complete one of the following:

I. Lab 2 Constructions (other than #9, the Tangent Envelope Project)

II. The Dollar Bill and Tangent Envelope Projects

III. The Pinwheel Unit

IV. The Star Unit

V.The Bisection and Trisection of Segments and Angles

Write each EFM in the following format:

Given _______(a)________ one can fold a line _______(b)________; the resulting line has the property that ______(c)_________ .

(a) Objects (lines and points) observed and used in making and describing the fold

(b) Description of the process of using the given objects to make the desired fold

(c) Consequent property(ies) of the resulting line in relation to the objects given

Why is creating a list of elementary folding moves hard? Well, for one thing, the objectives are hard to make clear. But even when the objectives begin to have more clarity, it's still hard because what we're doing is creating a mathematical model that is an abstractionof some real thing. And it's hard to know exactly what should be "abstracted out" of the real world - not that there's a unique solution!

Stage 2

Now that one EFM has been written, EFM 1: Given two points A and B, one can fold point A onto point B and you have identified another fold that cannot be accomplished by EFM 1, draft a second EFM so that the fold you identified as not fitting into the EFM 1 format can be accomplished by applying your new EFM.

Repeat the above, seeing if there is a third EFM needed for one of the class folding projects.

Send all new EFM's to me [jm].