Geometry is one of the most beautiful aspects of mathematics. This beauty is because you can "see" geometry at work. Most people are exposed to the very basic elements of geometry throughout their schooling with the most concentrated study in the secondary school curriculum. High schools in the United States offer one year of concentrated study of geometry that shows students how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. Unfortunately, as the course is only one year long, there is still very much in geometry left unexplored for the general audience. That is the challenge of this book, in which we will present a plethora of amazing geometric relationships. We begin with the special relationships of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationships between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry. Request Inspection Copy Sample Chapter(s) Introduction Chapter 9: Geometric Surprises Contents: About the Authors Introduction The Golden Ratio in Geometry Unexpected Concurrencies Unexpected Collinearities Squares on Triangle Sides Similar Triangles on Triangle Sides Discovering Concyclic Points Circle Wonders Polygons and Polygrams Geometric Surprises Geometric Fallacies Homothety, Similarity, and Applications Index Readership: This book is suitable for secondary/high school level students and teachers, as well as a general readership, particularly those interested in bridging the gaps in their knowledge of geometry.