When we measure, we use geometry. When we build, we use geometry. When we use a map, we use geometry. As societies have developed, they have seen the importance of geometry as they try to understand the motion of the stars, to parcel land, to mark the passage of time, to navigate - whether it be across a sea or to the moon.
Geometry is the mathematics of points, lines, angles, surfaces, and solids.
It allows us to describe, categorize, and measure these objects. By doing this, it provides a language to describe and analyze aspects of the world we see around us. Understanding the world requires that we recognize the underlying shapes in the physical world. Geometry involves absolute precision, which is an ideal that is only approximated by objects in the natural world but that ties together the similarities of these objects. The exactness of geometry is thus an abstraction, requiring exact arguments.