Scale factor

A scale factor is a number which scales, or multiplies, some quantity. In the equation Failed to parse (Missing texvc executable; please see math/README to configure.): y=Cx , Failed to parse (Missing texvc executable; please see math/README to configure.): C

is the scale factor for Failed to parse (Missing texvc executable; please see math/README to configure.): x

. Failed to parse (Missing texvc executable; please see math/README to configure.): C

is also the coefficient of Failed to parse (Missing texvc executable; please see math/README to configure.): x

, and may be called the constant of proportionality of Failed to parse (Missing texvc executable; please see math/README to configure.): y

to Failed to parse (Missing texvc executable; please see math/README to configure.): x

. For example, doubling distances corresponds to a scale factor of 2 for distance.

Applications

There is also a scale factor for the expansion of the Universe.

Computer Science

Scale factors are used in computer science when certain real world numbers need to be represented on a different scale in order to fit a required number format. See Scale Factor (Computer Science).

Geometry

A factor can be used to scale shapes in 1, 2, or 3 dimensions (and conceptually even more.) There are a few interesting properties of scaling which are relevant:

• The length of a line that is scaled is the previous length times the scale factor. In other words:

Failed to parse (Missing texvc executable; please see math/README to configure.): L_1 = L_0 \cdot c .

• The area of a shape in two-space (a circle, for example) is equal to the previous area times the square of the scale factor. In other words:

Failed to parse (Missing texvc executable; please see math/README to configure.): A_1 = A_0 \cdot c^2 .

• The volume of a shape in three-space is equal to the cube of the scale factor times the initial volume. In other words:

Failed to parse (Missing texvc executable; please see math/README to configure.): V_1 = V_0 \cdot c^3 .

• The scale factor also scales the coordinates of the centroid of a shape.
• The inverse of scaling a shape is scaling it again, with the reciprocal of the first factor.

See also

• Scale (ratio)
• Scale (map)
• Scales of scale models
• Scale (disambiguation)
• Scaling (geometry)
• Scalar (mathematics)
• Scaling in gravityhttp://en.wikilib.com/wiki/Orbit#Scaling_in_gravity

This mathematics-related article is a stub. You can help Wikipedia by expanding it.

es:Factores de escala

pl:Czynnik skali