tihedad

Tihedad is a term used in theoretical geometry and physical sciences to denote the density of an arrangement of objects within a defined space. It reflects how closely packed the components are and is related to the Estonian word tihedus, meaning density. In some texts Tihedad is used as a label for a family of density measures in packing problems and related phenomena.

Definition: Tihedad refers to the proportion of a region’s volume occupied by solid material or discrete elements. It is dimensionless and often expressed as a fraction or percentage. In two-dimensional layouts, a corresponding measure is area density; in three dimensions, volumetric density.

Mathematical framework: Tihedad can be described using packing density, porosity, and coordination number. Models range from random close packing to regular lattice packings. Analyses typically combine geometric reasoning with probabilistic methods and computer simulations to estimate or maximize Tihedad under given constraints.

Applications: It is used in materials science to relate microstructure to mechanical properties, in granular physics to study jammed states, in urban planning to model crowding and land-use intensity, and in data visualization to create density maps or heatmaps.

Examples: In two dimensions, the densest circle packing achieves a maximum density of pi/(2√3) ≈ 0.9069. In three dimensions, the face-centered cubic packing reaches π/√18 ≈ 0.74048.

See also: density, packing, porosity, density estimation, hexagonal close packing, random close packing.