Homework is due in class on Wednesdays.

Due September 30:  
1.2.1, 1.2.2;
1.3.3, 1.3.5;
1.4.1-3;
1.5.1-4.:w   (Hint: In 1.5.3, "m as small as possible" is a key condition.)

Due October 7:  
2.1.1, 2.1.2 (sketch the decomposition for regular n-gons, n = 3, ..., 6; you don't need to derive the general decomposition), 2.1.4;
2.2.1, 2.2.2;
2.3.2-5 (2.3.4 doesn't need to be elegant, and it can be computer generated, if that's easier for you);
2.4.2-4 (these exercises refer to Figure 2.11).

Due Wednesday, October 12:  
2.5.2-5;
3.2.4-6;
3.3.1-5;
3.4.1-3;
parallelograms exercise:

• Prepare instructions for creating a rectangle from a parallelogram using a single cut and reattachment, as was suggested in class Monday (not the multi-cut approach described in the text). Your instructions should be suitable for implememtation by someone with little or no mathematical training. Choose a scenario such as: lumberyard staff using a radial arm saw to cut plywood; art supply store staff using a mat cutter on foam core or gator board; copy store staff using a paper cutter on paper or cardboard. (N.B. The raised edge perpendicular to the cutting blade, used to align and stabilize the material to be cut, is called the "fence".) You don't need to specify how the piece is reattached, just which sides get attached to each other.
• Develop analogous instructions for constructing a parallelogram from a rectangle using a single cut and reattachment. Assuming that the rectangle is M x K, specify what side lengths L are possible for a parallelogram with side lengths M and L, and for one with side lengths K and L. Specify whether you're assuming that the angle of the cut can be set, or that a cut can be made through any two specified points on the material (with RAS's, I think you generally set the angle; with paper cutters I've used, you aim for the point.) You can assume that the rectangle fits on the available cutting surface.
• Scenario: You and two friends decide to dress up as parallelograms for Halloween this year. Your math-challenged friend is the one who's going to buy the foam core and have it cut and glued/taped. What instructions should you give him/her if they'll be buying 2' x 3' foam core boards and you want to have one parallelogram with all four side equal, one with one pair of sides of length of 3' and the other as long as possible, and one with one pair of sides of length of 2' and the other as long as possible? (One cut and reattachment per parallelogram, as above.) What geometrically relevant label(s) could you use to disguise/justify the seam?

Due Wednesday, October 19:  
3.5.1, 3.5.3-5;
3.6.1-4;
3.7.1-4;
4.1.1, 4.1.3;
4.3.1
Hint for 3.7.1-4: If you 'walk around' the triangle ABC, going from A to B to C back to A, are you walking clockwise or counter-clockwise? What about when you walk around f(A)f(B)f(C)?

Due Wednesday, October 26:  
4.4.1-4;
4.5.1-2;
4.6.1-4;
Find two examples of properly handled perspective in painting, sketches, etc.; find two badly handled examples. You can create your own examples if you're artistically inclined, but your bad examples shouldn't be just generally bad art - the perspective should be the main problem.
Some examples: You can look here for inspiration, but need to find your examples elsewhere. PhotoshopDisasters' perspective section has some fun examples. Less disastrous examples of digital manipulation of perspective in Photoshop are given in the tutorials architectural photo tutorial and landscape photo tutorial. David Hockney's photographic collages mess with perspective - the individual photos are shot from wildly different perspectives.
Google's Art Project is a fantastic source of images. You are very welcome to find your examples here.

Due Wednesday, November 2:  
5.1.1-3;
5.2.1-2;
5.3.1-4;
5.4.1-3;
5.5.1-3
 

Due Wednesday, November 9:  
5.6.1-4;
5.7.1-3;
exercises on linear fractional transformations from projections.

Due Wednesday, November 16:  
5.8.1-6;
7.1.1, 2;
7.2.2, 3, 5, 6;
7.3.1, 2.

Due Wednesday, November 23:  
7.4.1-6;
7.5.1.

Due Wednesday, November 30:  
8.1.1-4;
8.2.3 (use 8.2.1 and 2, but don't do them), 8.2.4-6.;
Exercises on cross products and the Cayley transform, plus additional exercises. Start on the cross products and Cayley exercises ASAP!

Homework teams
You are not only allowed, but encouraged, to work with classmates on the homework, and could divvy up the exercises among members of your study group. Unfortunately, it sounds like every team member needs to submit their own copy of the assignment.

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