Acknowledgements Acknowledgements

I am grateful for the sabbatical time Rivier University provided so that I could produce this book. The initial design and many of the activities for this textbook were created during my Spring 2016 sabbatical, and the book was written during my year-long sabbatical in 2023-2024. In addition, I appreciate the 2024 and 2025 Rivier Summer Faculty Research Grants that enabled me to recruit Rivier University student interns. The constructive feedback I received from the first group of student interns Sarah Frazier, Elisabeth Jacob, and Caitlyn St. Cyr exceeded my expectations. In addition, to identifying errors and dead links, they suggested rephrasings of sentences and identified where additional explanations, hints, or activities might be helpful. In the second summer, students Alexander Hagopian and Elisabeth Jacob added problems and figures, updated code, and improved the interactivity. I would also like to thank my MA127 Geometrical Explorations students over the years. Watching their teamwork, struggles, questioning, growth, and success has helped me revise these activities and transform them into a coherent text.

I thank the PROSE/PreTeXt community who made this format possible. Not only was the code available for use, they welcomed me as a new user, encouraged my project, and offered technical support. Steven Clontz, Oscar Levin, David Austin, and Chrissy Safranski were expecially helpful in helping me identify errors in my code, suggesting ways to yield desired outcomes, and introducing me to new features in PreTeXt. They, and other community members, took time out of their own busy schedules and made me feel welcome at their online office hours. I would also like to thank Rob Beezer and the other developers for creating and refining the PreTeXt markup language.

My own love of mathematics was sparked by people who encouraged me to explore. My parents, Paul and Patricia Deltz, provided a loving home filled with crafts, games, and puzzles. We were encouraged to play, experiment, and learn from our mistakes. My seventh-grade teacher, Crystal Mills at Saint Thomas More School (Houston) sparked my geometrical curiosity and creativity with her intriguing origami polyhedra decorating her classroom and her encouraging me to explore the paths of a billiard ball as a science project. At the University of Dallas, professors Dr. Andrew Berner and Dr. Charles Coppin engaged us in inquiry-based lessons. Their inspiration led me to continue my studies and shaped my own philosophy of teaching. My doctoral advisor, Dr. John Faulkner (the University of Virginia), guided my exploration relationships between geometric and nonassociative algebraic structures.

Naturally, this book has been influenced by my previous use of textbooks and my interactions with other mathematicians. Early iterations of this course used [2.6.1] or [2.6.2] and these sources influenced some activities here. The idea for the first chapter, using pentomino puzzles to motivate a study of area, most likely came from a derivative of Henri Piccioto’s work. These pentomino puzzles proved to be a perfect starting point: employing play as an entry point to a concept that would guide and unify the rest of my textbook.

Last but not least, I appreciate the love, support, and encouragement I’ve received from my family, especially my husband John and my son Paul. Paul also helped me as I struggled to use GitHub tools for the first time. It was a humbling and rewarding experience to learn from him; an experience I will always treasure.