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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).
The plate scale of a telescope connects the angular separation of an object with the linear separation of its image at the focal plane. If focal length f {\displaystyle f} is measured in mm, the plate scale in radians per mm is given by angular separation θ and the linear separation of the image at the focal plane s , or by simply the focal ...
Across all dimensions, a conformal linear transformation has the following properties: . Distance ratios are preserved by the transformation. [2]Given an orthonormal basis, a matrix representing the transformation must have each column the same magnitude and each pair of columns must be orthogonal.
Here is the ratio of magnification or dilation factor or scale factor or similitude ratio. 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 first four iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses the scale factor (S = 3) and the number of self-similar objects (N = 4) to calculate the dimension, D, after ...
Therefore, the shear factor m is the cotangent of the shear angle between the former verticals and the x-axis. (In the example on the right the square is tilted by 30°, so the shear angle is 60°.) (In the example on the right the square is tilted by 30°, so the shear angle is 60°.)
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In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...