azimuthalluku

Azimuthalluku is a hypothetical coordinate construct used in theoretical discussions of spherical geometry and data representation. It combines an azimuth angle with a discrete radial index, or luku, to encode a point on a sphere in a compact, stepped form. The term blends azimuth with a word suggesting number or count, signaling its numerical, discrete component.

Definition and framework. In the azimuthalluku system, a position on the unit sphere is described by a pair (A, L). A is the azimuth angle measured from a fixed reference meridian, typically within [0, 360) degrees. L is a nonnegative integer that specifies a radial layer or distance category from the center, rather than a continuous radius. The radial distance is drawn from a stepped scale, such as distance ≈ L · r0, where r0 is a chosen base unit, with possible refinements by additional indices for finer discretization.

Properties. The azimuthal coordinate behaves as in standard azimuthal descriptions: it records the angle around the central axis and is affected by rotations about that axis. The L index introduces discretization in the radial dimension, resulting in a set of concentric, discrete shells. This structure preserves angular relationships while replacing continuous radial distance with a finite set of layers, which can simplify certain computations or visualizations.

History and uses. Azimuthalluku is not part of official cartography or navigation; it is typically described in thought experiments, speculative fiction, or pedagogical illustrations of discrete coordinate systems. It can be used to explore how discretization of distance influences spherical mappings, sampling, or rendering.

Example. A point with azimuth A = 45 degrees and L = 2 lies in the second radial layer at that azimuth on the modeled sphere; the exact spatial interpretation depends on the chosen base unit r0.

See also. Azimuth, Spherical coordinates, Azimuthal projection, Discretization.