Many people have less-than-fond memories of learning geometry. What they remember most vividly is the proofs that they had to learn in high school. For most people this was an unpleasant experience in memorization of trivial statements in a particular sequence. Not only was this an unpleasant experience for them, but they also saw little purpose in it. If they ever thought to ask their teacher why they had to learn it they were told something like, "It's good for you to learn to think logically." Naturally, this answer did little to make the experience more pleasant. People with longer memories may remember their elementary school geometry experience. Their memories of this are usually somewhat more pleasant, as they remember learning shape names and names of geometric objects such as points, lines, line segments, arcs, and rays. But they still didn't gain much of a perspective on why it was important to learn geometry.

The field of geometry, as defined by NCTM, is very broad and has many applications. Analysis of two- and three-dimensional shapes and a study of geometric relationships are used in fields ranging from architecture to landscaping. An ability to specify locations and describe spatial relationships is used in everything from navigation to shipping, transportation, and construction. Transformations and symmetry are useful in a range of projects from packaging to artistic expression. The programming of computer graphics and the intuitive interface with computers that we all depend on were made possible through geometry. Furthermore, geometry can be seen as a conceptual glue that connects many different areas within mathematics. For example, shapes drawn on a coordinate grid can be analyzed in terms of algebraic relationships. Concepts such as area of a rectangle or volume of a rectangular solid can help with interpretation of bar graphs. Fractional amounts are most often represented using geometric shapes. Percents are often modeled with a square that is partitioned into one hundred small squares. As we begin to explore areas in which geometric knowledge and skill are useful we find an abundance of applications. It is difficult to imagine any area of mathematics that is more widely used than is geometry.