Non-Euclidean Adventures on the Lenart Sphere

• Introduce objectives
• Describe construction steps
• Guide student investigations
• Offer suggestions for additional exploration The activities review a traditional topic from planar geometry, then give the students directions to experiment with the same topic on the sphere. Students are challenged to shift their thinking from the plane to the sphere and to compare two different worlds of geometry. This book can serve as the text for a course in spherical geometry, or you can select individual investigations from the book to use in conjunction with any geometry text.
• Most activities deal with basic concepts of spherical geometry such as points, lines, circles, distance, angles, and area.
• Later investigations explore tessellations on the sphere and inscribed Platonic solids.
• Teachers notes provide advice and support for these activities. Non-Euclidean Adventures on the Lenart Sphere includes applications in which students create their own maps on a globe and construct the earths coordinate system. Students also follow routes taken by explorers and demonstrate the collision of the continental plates. We designed the activities in Non-Euclidean Adventures on the Lenart Sphere to be accessible to any teacher with a knowledge of traditional Euclidean planar geometry. You dont need any previous experience with spherical geometry to use this book.

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