afstandene

afstandene are the distances between points or objects. In Norwegian, afstandene is the definite plural form of avstand (distance), used across everyday language, geography, mathematics, and computer science to refer to multiple separations or the distances in a given context.

In mathematics and geometry, distance is a metric: a non-negative value that is zero only when the two points coincide, is symmetric, and satisfies the triangle inequality. In two-dimensional space, the distance between (x1, y1) and (x2, y2) is sqrt((x2 − x1)^2 + (y2 − y1)^2); in n dimensions this generalizes to sqrt(sum of squared coordinate differences). Other metrics exist, such as the Manhattan distance sum(|dx| + |dy| + ...), or the Chebyshev distance max(|dx|, |dy|, ...).

In geography and cartography, distances can be straight-line (geodesic) or along routes. The shortest path on the Earth's surface is a geodesic, often computed with haversine or Vincenty formulas. Distances are typically expressed in meters or kilometers and may refer to crow-fly distance, road distance, or travel time given a speed.

In computing and data analysis, distance functions measure similarity between objects. Common choices include Euclidean (L2), Manhattan (L1), and Chebyshev (L∞) distances, as well as Hamming distance for categorical data. The selected distance metric influences clustering, nearest-neighbor search, and many algorithms.