Non-Euclidean Adventures on the Lénárt Sphere

The high school geometry curriculum is primarily based on Euclidean concepts and constructions. Often, non-Euclidean ideas appear in high school geometry books as topological curiosities or historical asides, relegated to footnotes or visual activity boxes. Students are asked to consider these ideas only briefly if at all. Rarely is non-Euclidean geometry handled with the same depth or rigor that is used to study plane geometry. Even rarer are instances of non-Euclidean exploration with manipulatives.

This book is a collection of comparative geometry activities – or adventures – for students. Most of the adventures deal with the basic concepts of spherical geometry, such as points, lines, circles, distance, angle, and area. These concepts are compared and contrasted with the corresponding ideas of elementary plane geometry.

The adventures are presented in two forms to accommodate two different learning styles. First each adventure is succinctly described on an Adventure Card as an unguided investigation in which students determine their own paths of exploration. Then the same adventure is repeated in the more structured Student’s Guide with step-by-step constructions, guided investigations, and questions for further exploration. Following the Student’s Guide is the Teacher’s Guide with solutions and hints.