1. Geometry on a Ball Spherical Geometry… a Non-Euclidean Geometry

2. Children love spherical geometry

3. Study Guide • 1. Read pp 188,9 plus handout 3-6 • 2. What Great Circle is midway between N and S poles? • 3. Match gives locations N & latitude S of Equator • longitude gives locations E & W of Prime Meridian • 4. In Spherical Geo, lines = ??

4. Study Guide b • 5. Euclidean Geo Spherical Geo • System of: pts, lines, planes System of: pts, ? , ? • 6. What are Polar Points? • 7. Compare Euclid’s line to a Great Circle. • 8. Which of Euclid’s first five postulates are NOT in Spherical Geometry? • 9. How many lines go through a point parallel to another line in Spherical Geo? • 10. Great Circles have _____ collisions with other great circles?

5. Answers • 2. The Equator • 3. connect straight across… do not crisscross! • 4. Lines = Great Circles • 5. Points, Great Circles, and Spheres • 6. polar points are points on opposite sides of the ball…north and south poles… • 7. =; except that grt circles wrap around and overlap, touching…lines do not! • 8. the 5th postulate of Euclid is denied in Elliptic (Spherical) Geo • 9. 0 are parallel • 10. 2

6. Yes, we’re finished