Nwymiarowe

N-wymiarowe (nwymiarowe) is Polish for objects or spaces that require n independent directions to specify a position. The standard model is Euclidean n-space, denoted R^n, consisting of all ordered n-tuples (x1, ..., xn) with the usual distance d(x,y) = sqrt(sum (xi - yi)^2). The dimension n equals the number of coordinates and the minimal number of basis vectors needed to span the space.

In geometry and linear algebra, n-wymiarowe objects include polygons in 2D, polyhedra in 3D, and higher-dimensional analogues such as hypercubes and simplices. Projections, cross-sections, and linear or affine transformations can change, preserve, or reveal the dimension of these objects. The concept also extends to infinite-dimensional spaces studied in functional analysis and related fields.

Applications of nwymiarowe spaces appear across mathematics, physics, computer science, and data analysis. Spacetime is often described as 4-wymiarowy in relativity; 3D models are standard in computer graphics; high-dimensional feature spaces are common in machine learning and data mining. The dimension of an nwymiarowy object strongly influences its geometric, combinatorial, and analytic properties, and high dimensionality can give rise to phenomena such as the curse of dimensionality in computation and statistics.

Etymology and usage: in Polish, the adjective is formed from wymiar (dimension) and is commonly written as n-wymiarowy (or nwymiarowy) to denote “n-dimensional.”