Scale factor

From Wikipedia, the free encyclopedia

A scale factor is a number which scales, or multiplies, some quantity. In the equation y = Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x. For example, doubling distances corresponds to a scale factor of 2 for distance.

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

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).

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:

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:

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:

V_1 = V_0 \cdot c^3.

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