This lab should be completed by teams of 2 - 6 students.

1. Get a hold of a dictionary, in paper or on-line. (Copy-and-paste facility will be much appreciated as you go through steps 2 and 3 below.)

2. Look up the definition of line as a noun, find all definitions that are pertinent to our geometric use of line as a straight line (You may be referred to straight line.), and write them down.

3. The definition(s) you found in step 2 are all expressed in words, which are themselves in the dictionary (duh!). Look up the definition of each of those words, finding all definitions that seem pertinent to mathematical use, and write each of them down.

4. If you contined in this manner, what would eventually happen?

5. Take a look at the axiom systems listed on MATH 306, and click on Hilbert. David Hilbert was a mathematician who around 1900 developed, among many other things, an axiom system for plane geometry in order to eliminate deficiencies in Euclidean geometry that were at that time becoming more and more evident. How does Hilbert deal with the consequences of your observation in step 4 above?

Make a list of properties that a "good" collection of axioms for a mathematical system should have. See the reading on page 9 of Journey. You might also want to consider examples, such as the Euclidean postulates, the axioms of Hilbert that you looked at above, and the Elementary Folding Moves that you constructed in class and which can rightly be considered as axioms for a folding geometry.

E-mail me your list of (at least 3) properties by Monday, November 24.