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Such a scaling changes the diameter of an object by a factor between the scale factors, the area by a factor between the smallest and the largest product of two scale factors, and the volume by the product of all three. The scaling is uniform if and only if the scaling factors are equal (v x = v y = v z). If all except one of the scale factors ...
The scale factor is dimensionless, with counted from the birth of the universe and set to the present age of the universe: [4] giving the current value of as () or . The evolution of the scale factor is a dynamical question, determined by the equations of general relativity , which are presented in the case of a locally isotropic, locally ...
The absolute value of ad − bc is the area of the parallelogram, and thus represents the scale factor by which areas are transformed by A. The absolute value of the determinant together with the sign becomes the signed area of the parallelogram.
Solutions for the dependence of the scale factor with respect to time for universes dominated by each component can be found. In each we also have assumed that Ω 0,k ≈ 0, which is the same as assuming that the dominating source of energy density is approximately 1.
The surface area of this general ellipsoid can also be expressed in ... Simplifying the above formula using properties of R G, [5] ... where k is a scale factor, ...
at latitude 45° the scale factor is k = sec 45° ≈ 1.41, at latitude 60° the scale factor is k = sec 60° = 2, at latitude 80° the scale factor is k = sec 80° ≈ 5.76, at latitude 85° the scale factor is k = sec 85° ≈ 11.5. The area scale factor is the product of the parallel and meridian scales hk = sec 2 φ.
In each zone the scale factor of the central meridian reduces the diameter of the transverse cylinder to produce a secant projection with two standard lines, or lines of true scale, about 180 km on each side of, and about parallel to, the central meridian (Arc cos 0.9996 = 1.62° at the Equator). The scale is less than 1 inside the standard ...
This scale factor is defined as the theoretical value of the value obtained by dividing the required scale parameter by the asymptotic value of the statistic. Note that the scale factor depends on the distribution in question. For instance, in order to use the median absolute deviation (MAD) to estimate the standard deviation of the normal ...