Math 402, Spring 2007

This is part of Assignment #8. Using Geometry Explorer, work through Section 7.4 (excluding exercises 7.4.1, 7.4.2). Answer the following questions:

1. Out of all the Saccheri quadrilaterals you constructed, what was the smallest summit angle measurement? Sketch a picture of the quadrilateral (or print out).

2. Out of all the Saccheri quadrilaterals you constructed, what was the largest summit angle measurement? Sketch a picture of the quadrilateral.

3. Use Geometry Explorer to construct a line in hyperbolic space and a point not on the line. Then use Geometry Explorer to construct limiting parallels (see page 436). Just turn in a sketch or two of your work.

4. Use the same notation as exercise 7.3.11 for h and a(h). Use Geometry Explorer to construct many pictures of the type shown in the picture accompanying this exercise (you can construct just one and then drag around P and Q to get others). For each, measure h and a(h) and make a chart of these values. What patterns do you see in the chart? Any guesses on a formula for a(h) in terms of h?

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