Chapter 1 Introduction to Geometrical Thinking
Geometry is all around us; we find it in nature, architecture, art, games, and technology. Throughout history, humans have marveled upon geometrical patterns, investigated possibilities, developed geometrical tools, and shared these discoveries with others. Mathematicians use logic to confirm what they observe and to convince other scholars. The theorems and formulas that you have likely encountered in previous classes were developed and refined over the last two millennia.
Some of these formulas and theorems are worth knowing well; for example, basic area and volume formulas, the Pythagorean Theorem, arise frequently in applications and conversations. You can apply geometry to real-world problems, and you will become more literate by demonstrating a strong understanding of geometrical applications. However, memorization and application are not the primary goals of this course. After all, search engines, calculators, and artificial intelligence can recall formulas and perform calculations for us.
Of greater worth, is the ability to see the mathematics around us, to ask questions and seek understanding, to imagine and create, and to share our knowledge with others. In this first chapter and throughout the book, you will be encouraged to practice mathematical habits of mind that will enable you to learn new ideas and delve deeper into familiar topics. At the same time, we will be establishing some key geometrical ideas that will be revisited later in the course.
