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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



a concept in geometry. Geometric figures are said to be similar if they are identical in shape, regardless of whether they are identical in size. The figures F1 and F2 are similar if between their points a one-to-one correspondence can be established such that the ratio of the distances between any two pairs of corresponding points of F1 and F2 a constant k. This constant is called the similarity factor. The angles between corresponding lines of similar figures are equal. Thus, in Figure 1 ∠B1A11C1 = ∠B2A2C2 = ϕ. The ratio of the areas of bounded similar figures is equal to the square of the similarity factor, and the ratio of the volumes of similar solids is equal to the cube of the similarity factor.

Figure 1

A geometric transformation of the plane (or of space) such that all figures in the plane are transformed into similar figures with the same ratio of similitude is called a similarity transformation, which is a special case of an affine transformation. The set of all similarity transformations of the plane or of space forms a group. Any similarity transformation can be represented as the successive application of a homothetic transformation and a proper or improper motion.

The concept of similarity and similarity transformations are used in such engineering applications of geometry as modeling and drawing. For example, the operation of the pantograph is based on the concept of similarity.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
We calculated the similarities between the malware variants using eight different distance measures to generate similarity matrices and to identify the malware family by adopting visualisation of the distance scores.
Amid reports that the film has striking similarities with Secret Ballot, director-producer Anurag Kashyap came forward in support of Masurkar and reached out to Payami and film's producer Marco Muller to get their opinion.
* For the minimal similarities lower than 0.0303 there is no consistent classical matrix.
Knowing the correlation between the spatial and temporal similarities, performance of the DRT system can be improved in two ways.
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(88) Erickson held that the usually protectable expression of a melodic sequence had merged with the idea of assigning [pi]'s digits to musical notes, and accordingly found no infringement--all of the similarities between the two works were traceable to this idea.
This approach uses cosine similarity to identify the similarities between the documents and k-means clustering is applied to cluster the relevant document.
Convergence is defined as the development of increasing similarities between two partners/spouses over time.
Apart from these, the other similarities which emerge from X = 25 are similarities between Assamese and Bengali, Bengali and Hindi, Bengali and Odia, Gujarati and Kannada, Hindi and Kannada, Kannada and Malayalam, Kannada and Odia, Kannada and Tamil, Kashmiri and Punjabi, Konkani and Malayalam, Odia and Sanskrit, and Sanskrit and Urdu.
Nevertheless, future researchers could use well-validated multiple items for measuring perceived similarities.
Content-based measures compute similarities among objects by comparing the contents of the objects involved, such as texts and multimedia.
With similarities between GO terms calculated, the semantic similarity between two query gene products was often calculated using a mean-max rule [10].