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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.
For small objects, different methods are used that also depend upon determining size in units of wavelengths. For instance, in the case of a crystal, atomic spacings can be determined using X-ray diffraction. [13] The present best value for the lattice parameter of silicon, denoted a, is: [14] a = 543.102 0504(89) × 10 −12 m,
The listed objects currently include most objects in the asteroid belt and moons of the giant planets in this size range, but many newly discovered objects in the outer Solar System are missing, such as those included in the following reference. [58] Asteroid spectral types are mostly Tholen, but some might be SMASS.
Two congruent objects always have either the same shape or mirror image shapes, and have the same size. Objects that have the same shape or mirror image shapes are called geometrically similar, whether or not they have the same size. Thus, objects that can be transformed into each other by rigid transformations, mirroring, and uniform scaling ...
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines , are statistically self-similar: parts of them show the same statistical properties at many scales. [ 2 ]
Similarity measures play a crucial role in many clustering techniques, as they are used to determine how closely related two data points are and whether they should be grouped together in the same cluster. A similarity measure can take many different forms depending on the type of data being clustered and the specific problem being solved.
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Indeed, Dedekind defined an infinite set as one that can be placed into a one-to-one correspondence with a strict subset (that is, having the same size in Cantor's sense); this notion of infinity is called Dedekind infinite. Cantor introduced the cardinal numbers, and showed—according to his bijection-based definition of size—that some ...