Similarity

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Similarity

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.

References in periodicals archive ?
Also, epigenetic super-similarity is a previously unrecognised phenomenon that may contribute to the phenotypic similarity of monozygotic twins, according to the study.
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This Article seeks to bring analytical clarity to copyright's similarity analysis, with a focus on these often-implicit framing issues.
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The application of fuzzy numbers in resolving problems requires the application of different similarity measures, calculating the degree of similarity between two fuzzy number; similarity measures appropriate for solving one type of problem often are not appropriate for solving the other problem or type of problems.
Furthermore, a new similarity of BPAs is proposed based on the modified cosine similarity, which is used to measure the degree of conflict.
In general, perceived similarity to a particular group can lead individuals to consider media as having a similar amount of influence on those individuals and on the particular group.
In the literature, there are few researchers who studied the distance and similarity measure of IVNS.
7) Instead, it comes into play--at least in theory--in every single judicial determination of copyright infringement, through the requirement of "substantial similarity.
The first description of a sequence similarity search method that allows insertions, deletions, and gaps was published in [Needleman, 1970] where a computer program for finding similarities in the amino acid sequences of two proteins was developed.

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