Geometry by Construction: Object Creation and Problem-solving in Euclidean and Non-Euclidean Geometries

Geometry by Construction: Object Creation and Problem-Solving in Euclidean and Non-Euclidean Geometries offers a hands-on, exploratory approach to geometry for college students, educators, and secondary teachers. The book blends classical Euclidean concepts with non-Euclidean models, encouraging readers to create geometric objects, construct proofs, and reason through results independently.

Organized into three rich chapters, it spans standard Euclidean topics and “bent” space explorations where some Euclidean rules change. With exercises ranging from foundational problems to new research-level questions, the text supports learning across high school, undergraduate courses, and research experiences. Emphasizing constructions, active engagement, and creative problem-solving, it provides a unique environment for understanding geometry beyond formulas, fostering skills in reasoning, visualization, and mathematical exploration.

This resource is ideal for students and teachers seeking a dynamic, interactive approach to learning geometry, bridging traditional methods with modern explorations in Euclidean and non-Euclidean spaces.