Chapter

Geometry and Geography

From Quantitative Problem Solving in Natural Resources by Peter Moore

Concepts

1. Length Area

   "Length is a one-dimensional quantity with dimensions of [L], area is two-dimensional with dimensions of [L²], and volume is three-dimensional with dimensions of [L³]. These distinctions matter becaus

2. Must Spatial

   "When converting lengths, the conversion factor is used once; when converting areas, it must be squared; and when converting volumes, it must be cubed. This follows from the number of spatial dimensio

3. Map Scale

   "A map scale is a dimensionless proportion relating a distance on a map to the corresponding distance in the real world. The units may be chosen freely as long as the same units are used on both sides

4. Geometric Idealization

   "When a natural object is difficult to measure directly, it can be approximated using a simple geometric shape such as a cylinder, sphere, rectangle, or polygon. The approximation can provide a ballpa

5. Polygon Areas

   "An irregular polygon can be divided conceptually into trapezoids using the coordinate pairs of its vertices in a Cartesian system. The areas of the trapezoids are calculated and summed, with negative