No.	Assignment Due	Page and No.'s
#1	Tuesday Jan. 22	Provide a Model of a 3-pt geometry in terms of vertices and edges. Page 9:  1, 2, 3, 4, 7 Referring to Problem #7, use vertices and edges to provide a model of the "four-line geometry".   (Hint: think of straight lines in the Euclidean plane, no three of which intersect in a common point.)
#2	Thursday Jan. 31	Page 17 (Cederberg): 1,3,5,6,8,9 (note that #10 is postponed). Given two statements p and q, provide a Truth Table for the statment "Both p and q are true". Extra Credit - Page 17: #2
#3	Thursday Feb. 7	In an affine plane of order n, prove that given any line l with k points and any point P not on the line l, there are exactly k+1 lines incident to P. Page 18 (Cederberg): 10,11,14,16.
#4	Tuesday Feb. 26	Page 24 (Cederberg): 3,6,8,9
#5	Thursday Feb. 28	Use SketchPad to illustrate Desargues' Theorem. (a) Draw a point P, a triangle ABC and another triangle A'B'C' which is in perspective to ABC relative to P. (b) Construct the perspective line, by drawing a line between any two of the intersection points. Notice that this perspective line passes through the third intersection point. (c) Hide any unnecessary points/lines and format the lines to make the theorem clearer.
#6	Tuesday Mar 4	Page 29 (Cederberg): 3,4. # 8 [Extra Credit] For Problem 8, you may refer to the marked-up model or prove it using the results of this section. Two higher resolution pdf's for the Desargues' configuration may be found by clicking the two thumbnail images:
#7	Thursday Apr 3	Prove Pappus' theorem for the parallel configuration: ( i.e. Problem 1.4.3 of the Chapter 1 of the reference. Assigned in class - 25 pts) Given a length a, construct a right triangle with hypothenuse of that length. Given two squares, construct another square whose area is the sum of the areas of two given squares. If a quadrilateral (polygon with 4 sides) has its vertices on a circle, show that its opposite angles sum to pi. Consider the pentagon in figure 2.20 of Chapter 2 of the reference. (You may use the conclusion of Exercises 2.8.1 and 2.8.2 without proving them.) First describe the steps to construct the length x=(1+srt(5))/2 using only a ruler and a compass. Next, describe the steps needed, using this length and ruler/compass, to construct a pentagon with unit side length.

   Course Resources