Geometry on a Geometry on a BallBall

Spherical Geometry…Spherical Geometry… a Non-Euclidean Geometrya Non-Euclidean Geometry

Children love Children love spherical spherical geometrygeometry

Study GuideStudy Guide1. Read pp 188,9 plus handout 3-61. Read pp 188,9 plus handout 3-62. What Great Circle is midway between N 2. What Great Circle is midway between N and S poles?and S poles?3. Match 3. Match gives gives locations N & locations N & latitude latitude S S of Equatorof Equator longitude longitude gives gives locations E & locations E & W of Prime W of Prime MeridianMeridian4. In Spherical Geo, lines = ??4. In Spherical Geo, lines = ??

Study Guide bStudy Guide b5. Euclidean Geo5. Euclidean Geo Spherical GeoSpherical Geo

System of: pts, lines, planes System of: System of: pts, lines, planes System of: pts, ? , ? pts, ? , ?

6. What are Polar Points?6. What are Polar Points?

7. Compare Euclid’s line to a Great Circle.7. Compare Euclid’s line to a Great Circle.

8. Which of Euclid’s first five postulates are NOT in 8. Which of Euclid’s first five postulates are NOT in Spherical Geometry?Spherical Geometry?

9. How many lines go through a point parallel to 9. How many lines go through a point parallel to another line in Spherical Geo?another line in Spherical Geo?

10. Great Circles have _____ collisions with other 10. Great Circles have _____ collisions with other great circles? great circles?

AnswersAnswers2. The Equator2. The Equator

3. connect straight across… do not crisscross!3. connect straight across… do not crisscross!

4. Lines = Great Circles4. Lines = Great Circles

5. Points, Great Circles, and Spheres5. Points, Great Circles, and Spheres

6. polar points are points on opposite sides of the ball…north and 6. polar points are points on opposite sides of the ball…north and south poles…south poles…

7. =; except that grt circles wrap around and overlap, touching…7. =; except that grt circles wrap around and overlap, touching…lines do not!lines do not!

8. the 58. the 5thth postulate of Euclid is denied in Elliptic (Spherical) Geo postulate of Euclid is denied in Elliptic (Spherical) Geo

9. 0 are parallel9. 0 are parallel

10. 2 10. 2

Yes, we’re Yes, we’re finishedfinished