bidimensionale

Bidimensionale is an Italian term meaning two-dimensional. It describes objects, spaces, and representations that have two independent directions or axes, typically length and width, forming a plane. In mathematics, a bidimensional space is a two-dimensional Euclidean space, commonly denoted R2, consisting of all ordered pairs (x, y). The distance between points is defined by the Euclidean metric, d((x1, y1), (x2, y2)) = sqrt((x1 − x2)² + (y1 − y2)²). Areas are computed by planar geometry, and many theorems concern planar figures such as lines, circles, and polygons.

Coordinate systems are central to bidimensional spaces. The most common is Cartesian coordinates (x, y). Other systems include polar coordinates (r, θ), with x = r cos θ and y = r sin θ. Points can also be represented as vectors, and plane transformations are described by 2×2 matrices for linear parts, or 3×3 homogeneous matrices to incorporate translations.

In computing and digital media, the term bidimensionale often refers to two-dimensional representations. A digital image is a bidimensional array of pixels, indexed by rows and columns. Two-dimensional graphics include both vector scenes projected onto a plane and raster images composed of a grid of picture elements.

Applications of bidimensional concepts span computer graphics, computer-aided design, geographic information systems, and physics, particularly for problems constrained to a plane or surface. In higher mathematics, bidimensional ideas extend to 2D manifolds and surfaces studied within topology and differential geometry.