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Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
A scale factor of 1 ⁄ 10 cannot be used here, because scaling 160 by 1 ⁄ 10 gives 16, which is greater than the greatest value that can be stored in this fixed-point format. However, 1 ⁄ 11 will work as a scale factor, because the maximum scaled value, 160 ⁄ 11 = 14. 54, fits within this range. Given this set:
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 ...
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.
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 ...
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With the scale-factor cutoff shown by the gray dotted lines, only observers who exist before the region has expanded by the scale factor are counted, giving normal observers (blue) time to dominate the measure, while the left-hand universe hits the scale cutoff even before it exits inflation in this example. [3]
The scale factors for the elliptic coordinates (,) are equal to = = + = . Using the double argument identities for hyperbolic functions and trigonometric functions, the scale factors can be equivalently expressed as