1by2

1by2 refers to a rectangle with sides measuring 1 and 2 units, commonly written as 1×2. In mathematics, this shape is known as a domino, the simplest non-square polyomino, and it serves as a fundamental building block in tiling problems and combinatorial studies.

In tiling theory, the 1×2 rectangle is used to cover larger regions on a square grid without overlaps or gaps. Dominoes may be placed horizontally or vertically, depending on the region’s boundaries. A classical result concerns tiling a 2×n rectangle: the number of distinct tilings by 2×1 dominoes satisfies the recurrence T(n) = T(n−1) + T(n−2), with T(0) = 1 and T(1) = 1. Consequently, the count of tilings for 2×n boards equals the (n+1)th Fibonacci number. This connection to Fibonacci numbers and transfer-matrix methods highlights the role of 1×2 rectangles in combinatorics and mathematical proof techniques.

Beyond theory, 1×2 rectangles appear in practical contexts such as domino games, floor and wall tiling patterns, and grid-based design or pixel art where compositions are built from 1×2 units. The term is also used in product naming and design to denote items sized 1 by 2 units.

In sum, 1by2 denotes a basic domino shape that underpins both theoretical tiling problems and a range of applied patterns and games, illustrating how a simple rectangle can yield rich mathematical and practical insights.