Scale factor


Scale factor

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.

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: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.
*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.

ee also

* Scale (ratio)
* Scale (map)
* Scales of scale models
* Scale (disambiguation)
* Scaling (geometry)
* Scalar (mathematics)
*
* Scaling in statistical estimation
* Scale factor (Universe)


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