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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).
Two congruent shapes are similar, with a scale factor of 1. However, some school textbooks specifically exclude congruent triangles from their definition of similar triangles by insisting that the sizes must be different if the triangles are to qualify as similar. [citation needed]
The scale factors for (,,) are: = + + = + = (+) () Knowing the scale factors, various functions of the coordinates can be calculated by the general method outlined in the orthogonal coordinates article.
In computer science, a scale factor is a number used as a multiplier to represent a number on a different scale, functioning similarly to an exponent in mathematics. A scale factor is used when a real-world set of numbers needs to be represented on a different scale in order to fit a specific number format .
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
Such a transformation can be called an enlargement if the scale factor exceeds 1. The above-mentioned fixed point S is called homothetic center or center of similarity or center of similitude . The term, coined by French mathematician Michel Chasles , is derived from two Greek elements: the prefix homo- ( όμο ' similar ' }; and transl. grc ...