This book presents 125 unusual geometric relationships, offering clear proofs that will captivate readers of all backgrounds. Geometry is one of the most visually compelling and surprising branches of mathematics, full of unexpected relationships that are easy to see but astonishing to uncover. From the concurrency of triangle lines — medians, altitudes, and bisectors — to the mysterious parallelogram hidden in any quadrilateral, the discoveries explored in this volume reveal the intuitive and exciting nature of geometry.To ensure all readers can fully appreciate these ideas, the opening chapters serve as a refresher on key high school geometry concepts, such as tangents and trigonometry, as well as powerful but often-overlooked theorems such as those by Ptolemy, Ceva, and Apollonius. With these tools in hand, you'll be ready to explore remarkable relationships that will deepen your appreciation for geometry. Whether you're a student, teacher, or math enthusiast, this collection will inspire fresh curiosity and excitement. Prepare to be amazed!

Table of Contents

Chapter 1 The Basic Elements of Geometry

Chapter 2 Spectacular Named Relationships in Geometry

Chapter 3 Applications of Some Named Geometric Relationships

Chapter 4 Properties of Components of Triangles

Chapter 5 Unusual Geometric Experiences

Chapter 6 Proofs of the Geometricks

About the Author

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.