6 Geometry Concepts
This chapter covers
- Recognizing what geometry problems are in the context of USACO.
- Breaking down geometry concepts that appear in USACO problems about searching and modeling.
- Solving geometry problems in one and two dimensions that involve points, lines, line segments, rectangles, and coordinate grids.
- Using and calculating Manhattan distance.
- Analyzing problems that include a circle as a geometric concept, and applying the appropriate concepts and tools.
- Recognizing geometric concepts for more involved shapes and settings, such as the perimeter of an enclosed area.
Geometry problems rely on coordinates to describe a configuration in space. At the Bronze level, these problems are typically limited to dealing with basic geometric shapes such as lines, line segments, rectangles, and two-dimensional grids. As such, the quantities of interest are often distance and area. There are, of course, exceptions to this generalization. For example, some problems require you to find the perimeter of a two-dimensional shape, or the direction of travel on a grid, or even the number of possible paths. The key to all these problems is a strong grasp of the one- and two-dimensional concepts that they’re built on.