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High school geometry books usually mention non-Euclidean geometry as a historical aside if at all. This is partly because until now students haven't had the tools to successfully visualize and investigate geometry on surfaces other than the plane.
Yet most surfaces, including our own planet earth, are not flat. It's important for students to realize that our familiar Euclidean geometry is not the only possible geometry. There are surfaces so different from the plane that lines are never parallel and triangles can have three right angles. Now, for the first time, middle and high school students can investigate spherical geometry using the Lénárt Sphere geometry construction materials and use a real sphere and the spherical equivalents of a compass and straightedge. With these new tools, students can compare and contrast relationships on the sphere with the corresponding relationships of Euclidean geometry. So by exploring first-hand an important non-Euclidean geometry, they'll also deepen their insights into the traditional geometry of the plane.
Investigating spherical geometry requires students to think creatively. And hands-on work with the Lénárt Sphere is a great opportunity for students to increase their spatial visualization skills. Spherical geometry also has many real-world applications—just ask any engineer, physicist, astronomer, or global navigator.
Invigorate Your Geometry Classes!
Once you see how much fun it is to investigate geometry on the sphere, you'll make the Lénárt 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 Lénárt Sphere gives students a tool to develop and test ideas in a new geometric system.
You Need a Sphere to Study Spherical Geometry