Surprising Geometric Solutions: A Projective Geometry Approach (Problem Solving in Mathematics and Beyond) - Hardcover

Posamentier, Alfred S; Stuhlpfarrer, David

Hardcover

ISBN 10: 9819831830 ISBN 13: 9789819831838

Publisher: WSPC, 2026

Synopsis

This book introduces the major ideas of projective geometry through clear explanations, visual intuition, and hands-on problem solving. Projective geometry opens a window into the deeper patterns of space, perspective, and form. While Euclidean geometry guides familiar constructions—drawing points, lines, and circles with a straightedge and compass—projective geometry goes further, encompassing hyperbolic and elliptic geometries and revealing the rules behind the way we see the world. Why do railway tracks appear to converge in the distance? Why does a tilted coin look like an ellipse? These are not illusions—they are manifestations of projective geometry at work.

Readers will explore classical constructions and fundamental geometrical ideas through a fresh lens, building towards an exploration of key projective principles such as duality and invariance. Highlighting real-world applications in mathematics, physics, computer science, art and architecture, the book presents projective geometry not just as a mathematical discipline, but as a way of seeing. Whether you are a student, teacher, or curious mind, this book offers a new perspective on geometry—not just what we measure, but how we perceive and understand the world around us.

About this title

About the Authors

Alfred S Posamentier is currently a Distinguished Lecturer at New York City College of Technology of the City University of New York. Previously, he was the Executive Director for Internationalization and Sponsored Programs at Long Island University, New York. This was preceded by a five-year period where he was Dean of the School of Education and tenured Professor of Mathematics Education at Mercy University, New York. He is now also Professor Emeritus of Mathematics Education at the City College of the City University of New York, and former Dean of the School of Education, where he was tenured for 40 years. Dr Posamentier is the author and co-author of more than 90 mathematics books for teachers, secondary and elementary school students, as well as the general readership, and is a frequent commentator in newspapers and journals on topics related to education.

David Stuhlpfarrer is an Austrian mathematician and mathematics educator with a strong focus on geometry, spatial reasoning, and the didactics of mathematics. His academic and professional career combines long-standing experience in secondary education with extensive involvement in teacher education, educational research, and national quality assurance initiatives. He studied Mathematics and Descriptive Geometry at Graz University of Technology and the University of Graz, earning a Mag. rer. nat., and later completed a PhD in subject didactics with distinction. His doctoral research focused on the relationship between spatial ability and mathematical achievement at the end of lower secondary education. Since 2008, he has taught mathematics and geometry at secondary schools and various vocational and adult education and higher education institutions. He has also served as a trainer, examiner, and mentor in adult education. He has contributed to national assessments in mathematics and competence-oriented evaluations, and is active in professional networks. His publications focus on geometry education, spatial reasoning, inquiry-based learning, and integrating digital and physical tools in mathematics instruction. Since 2020, he has been a faculty member at the University College of Teacher Education Styria, Austria, where he is involved in both pre-service and in-service teacher education for mathematics and geometry at the secondary level.

Edition details

• Publisher: WSPC
• Publication date: 2026
• Language: English
• ISBN 10: 9819831830
• ISBN 13: 9789819831838
• Binding: Hardcover
• Number of pages: 176