Preface to
Explorations in Geometry

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This book contains twelve explorations that are suitable to use as enrichment for a high school geometry course or a general education college mathematics course.  The topics included in the explorations are not the core topics that are usually included in a geometry course.  They are, however, ones that I (and hopefully the students) find intrinsically interesting.

In writing these explorations, I attempted to tell as little as was needed and to ask as much as I could.  My goal is for the students to discover concepts for themselves.  To do this, I have short explanations in each exploration where I introduce a topic, explain terms, and perhaps give an example.  This is immediately followed by questions.  These questions are interspersed in the narrative and are not located at the end of each section like a typical text.  Some of the questions ask students to do something quite similar to what was explained and some ask the students to go quite a bit further than what was explained.

I envision students working in small groups of two or three to answer the questions in the explorations.  I think more can be learned by working in a small group than from either a large class or individually.  However, some students prefer to work individually and they certainly could complete the questions doing so.

In a previous book that I coauthored, Understanding our Quantitative World, we wrote in the preface that that book addresses the question, “What mathematical skills and concepts are useful for informed citizens?”  In this book, my goal was to address the question, “What mathematics is most interesting and beautiful to explore?”  No attempt was made to try to show the usefulness of mathematics, but a great attempt was made to have students see the beauty in mathematics.