Search results
Results from the WOW.Com Content Network
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).
Scaling (geometry), a linear transformation that enlarges or diminishes objects; Scale invariance, a feature of objects or laws that do not change if scales of length, energy, or other variables are multiplied by a common factor Scaling law, a law that describes the scale invariance found in many natural phenomena
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual terms in the equations is determined.
Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.
Multifractal scaling: characterized by more than one fractal dimension or scaling rule; Fine or detailed structure at arbitrarily small scales. A consequence of this structure is fractals may have emergent properties [43] (related to the next criterion in this list).
Scaling (geometry) a similar notion in vector spaces Homothetic center , the center of a homothetic transformation taking one of a pair of shapes into the other The Hadwiger conjecture on the number of strictly smaller homothetic copies of a convex body that may be needed to cover it
Most common geometric transformations that keep the origin fixed are linear, including rotation, scaling, shearing, reflection, and orthogonal projection; if an affine transformation is not a pure translation it keeps some point fixed, and that point can be chosen as origin to make the transformation linear. In two dimensions, linear ...
The terms fractal dimension and fractal were coined by Mandelbrot in 1975, [16] about a decade after he published his paper on self-similarity in the coastline of Britain. . Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them in a new way to study complex geometries that defied description in ...