* Sscalar field *. The concept of scalar field dates from the 19th century and its application is oriented to the description of phenomena related to the distribution of temperatures within a body, the pressures inside fluids, the electrostatic potential, the potential energy in a gravitational system, population densities or of any magnitude the nature of which can approximate a continuous distribution.

**Summary**

[ hide ]- 1 in mathematics
- 2 Representation
- 3 See also
- 4 Source

**In math**

A scalar field associates a scalar value to each point in space. The value can be a mathematical number or a physical quantity. Scalar fields are often used in physics, in particular, to indicate temperature distribution across space, or air pressure.

Physically a scalar field represents the spatial distribution of a scalar magnitude.

Mathematically a scalar field is a scalar function of the coordinates whose physical representation is shown in Figure 1

The representations of these fields in a three-dimensional space require four dimensions, making it impossible to graph them in three dimensions, but they can be used as optimization tools for modeling cases where different variables intervene.

**Representation**

Scalar fields are represented by the function that defines them or by equipotential lines or surfaces.

An equipotential surface or line is defined as the locus of points such that: Φ = cte On a relief map, for example, there is a scalar field corresponding to elevation above sea level as a function of the latitude and geographic longitude coordinates. This case corresponds to a scalar field defined in two mathematical dimensions.

In this case, the equipotential surfaces are called contour lines, and as it follows from the definition, all the points belonging to a contour line have the same elevation above sea level.