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A scale factor is usually a decimal 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 two for distance, while cutting a cake in half results ...
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, [1] [2] when the rectangle is oriented as a "landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do ...
A golden rectangle with long side a + b and short side a can be divided into two pieces: a similar golden rectangle (shaded red, right) with long side a and short side b and a square (shaded blue, left) with sides of length a. This illustrates the relationship a + b / a = a / b = φ.
Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. [1] In such cases the scale is dimensionless and exact throughout the model or drawing. The scale can be expressed in four ways: in words (a lexical scale), as a ratio, as a fraction and as a graphical (bar) scale.
The ratio of the width to the height of an image is known as the aspect ratio, or more precisely the display aspect ratio (DAR) – the aspect ratio of the image as displayed; for TV, DAR was traditionally 4:3 (a.k.a. fullscreen), with 16:9 (a.k.a. widescreen) now the standard for HDTV.
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The fact that a rectangle of aspect ratio ρ 2 can be used for dissections of a square into similar rectangles is equivalent to an algebraic property of the number ρ 2 related to the Routh–Hurwitz theorem: all of its conjugates have positive real part.