Lenart Sphere & Non-Euclidean Geometry
Lenart Sphere
Lenart Sphere Basic Set

your price = $89.95



  • Investigate the geometry of our planet Earth (spherical or non-Euclidean geometry) using the Lenart Sphere.
  • Compare and contrast relationships on the sphere with corresponding relationships on flat surfaces.
  • Gain deeper insight into the traditional geometry of flat surfaces (the plane)
  • Increase your spatial visualization skills.

Note to Geometry teachers:
Once you see how much fun it is to investigate geometry on the sphere, you'll make the Lenart Sphere a regular part of your geometry program. When your students finish a geometric investigation on the plane, ask them what happens on the sphere. Is the result the same or different? Why? Because few students have worked with non-Euclidean geometry, their thinking will be fresh, their ideas original, and their results truly surprising. The Lenart Sphere gives you a tool to develop and test ideas in the new geometric system. Imagine learning plane geometry without a flat surface to draw on. It's just as hard to learn spherical geometry without drawing on a sphere.

What's included in the Lenart Sphere Basic Set:
  • A transparent plastic, eight-inch sphere
  • A ring-shaped support to place under the sphere
  • Four hemispherical transparencies that fit over the sphere so that students can draw on these with colored markers and cut out shapes with scissors
  • A spherical ruler with two scaled edges for drawing and measuring arcs, angles, and great circles on the sphere
  • A spherical compass and center locator for drawing circles on the sphere
  • A set of transparency markers for writing and drawing on the sphere and transparencies
  • A hanger for displaying your spherical constructions and designs
  • A 16-page booklet, Getting Started on the Lenart Sphere, with activities you can begin as soon as you open the box
  • A four-color polyconic projection of the earth that you can cut out and transform into your own globe



Lenart Sphere book Non-Euclidean Adventures on the Lenart Sphere
by Istvan Lenart

224 Pages. ISBN 1-55953-103-7.

Grade 6 through adult.

             your price = $39.95



Printed in Hungary on non-perforated pages.




Oriented toward the classroom or home-school setting, the blackline master book is your guide to introducing the Lenart Sphere in a classroom. Over 40 activity masters introduce objectives, describe construction steps, guide student investigations, and offer suggestions for additional exploration. The activities review a traditional topic from plane 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 plane 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. Teacher's notes provide advice and support for these activities.

Applications are included in which students create their own maps on a globe and construct the earth's coordinate system. Students also follow routes taken by explorers and demonstrate the collision of the continental plates.

No previous knowledge of spherical geometry is required. Activities are designed to be accessible to any teacher with a knowledge of traditional Euclidean plane geometry. You don't need any previous experience with spherical geometry to use this book.




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