threerectangle

Threerectangle is a nonstandard term used to describe a figure formed by the union of three rectangles in the plane. It is not part of a fixed formal theory, and its precise meaning varies by context. In many discussions, threerectangle refers to a connected union of three axis-aligned rectangles, with the arrangement of their sides determining the shape.

Common configurations include: a chain or straight configuration, where each rectangle shares a full side with the next; and branching configurations such as L- or T-shaped outlines, where the rectangles meet along partial edges or at a common corner. Rectangles may also overlap, rather than merely touch, complicating the boundary. The outer boundary is typically a rectilinear polygon, whose number of vertices depends on how the rectangles meet.

Properties of a threerectangle depend on how the pieces interact. The area of the union equals the sum of the individual areas minus the areas of overlaps (inclusion–exclusion if overlaps exist). The perimeter follows from tracing the boundary of the union and can vary widely with arrangement. For fixed rectangle sizes, different configurations yield different shapes and perimeters; conversely, for a given shape, the three constituent rectangles are not uniquely determined.

Applications and usage are mostly in informal discussions, puzzles, floor-planning exercises, and introductory geometry examples. The term serves as a simple building block for illustrating concepts in polygon union, rectilinear shapes, and constructive tiling, rather than as a formal object with a standardized set of theorems.

See also: Rectilinear polygon, Polyomino, Rectangular decomposition, Triomino.