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

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Presentation transcript:

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

Children love spherical geometry

Study Guide 1. Read pp 188,9 plus handout 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 longitude gives locations E & W of Prime Meridian 4. In Spherical Geo, lines = ??

Study Guide b 5. Euclidean GeoSpherical 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?

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 5 th postulate of Euclid is denied in Elliptic (Spherical) Geo 9. 0 are parallel 10. 2

Yes, we’re finished