Density

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:

where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight.

For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser.

To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water.

Density (polytope)

In geometry, the density of a polytope represents the number of windings of a polytope, particularly a uniform or regular polytope, around its center. It can be visually determined by counting the minimum number of facet or face crossings of a ray from the center to infinity. The density is constant across any continuous interior region of a polytope that crosses no facets. For a non-self-intersecting (acoptic) polytope, the density is 1.

Tessellations with overlapping faces can similarly define density as the number of coverings of faces over any given point.

Polygons

The density of a star polygon is the number of times that the polygonal boundary winds around its center; it is the winding number of the boundary around the central point.

For a regular star polygon {p/q}, the density is q.

It can be visually determined by counting the minimum number of edge crossings of a ray from the center to infinity.

Polyhedra

Arthur Cayley used density as a way to modify Euler's polyhedron formula (V − E + F = 2) to work for the regular star polyhedra, where d_v is the density of a vertex figure, d_f of a face and D of the polyhedron as a whole:

Density (disambiguation)

Density and dense usually refer to a measure of how much of some entity is within a fixed amount of space. Types of density include:

Physics

Density of mass

Densities of other entities