Read Sved Chapter 4 and Learn about the P-model in Chapter 5.
Construct the following in the Poincare model with GSP or by hand and turn in. Also, be prepared to explain or carry out any of these constructions on the Final Exam.
All points are P-points and all lines are P-lines unless otherwise specified.
2. For a point C not on line AB, construct the two lines through C that are converging parallel to line AB.
3. For a point C not on line AB, construct the line through C perpendicular to line AB.
4. For a point C not on line AB, construct the reflection of C in line AB.
5. For two (random) points A and B, construct the perpendicular bisector of AB.
6. Construct two ultraparallel lines and then construct the common perpendicular to these lines.
In this section, you will construct the circle with center A through B in each of several geometries.
Euclidean: In a plane, draw A and B, construct the E-circle c with E-center A through B.
DWEG: In a plane, draw the point O removed from the plane, and draw A and B. Construct the D-circle d with D-center A through B
Stereographic map: In a plane, draw a circle e that is the sterographic image of the "equator" on a sphere. Draw A and B. Construct the S-circle f with S-center A through B. In other words, f is the image of the circle on the sphere whose center maps to A and a point of which maps to B.
Poincare Model: In a plane, draw the P-disk bounded by h, and draw A and B. Construct the P-circle d with P-center A through B.
Question: What is common about all these circles. Write a short description explaining in what way they are the same and how the same construction tools can be used for each.