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Any two equilateral triangles are similar. Two triangles, both similar to a third triangle, are similar to each other (transitivity of similarity of triangles). Corresponding altitudes of similar triangles have the same ratio as the corresponding sides. Two right triangles are similar if the hypotenuse and one other side have lengths in the ...
To compare is to bring two or more things together (physically or in contemplation) and to examine them systematically, identifying similarities and differences among them. Comparison has a different meaning within each framework of study. Any exploration of the similarities or differences of two or more units is a comparison.
Similarity comes in degrees: e.g. oranges are more similar to apples than to the moon. It is traditionally seen as an internal relation and analyzed in terms of shared properties: two things are similar because they have a property in common. [1] The more properties they share, the more similar they are.
Similarity is an equivalence relation on the space of square matrices. Because matrices are similar if and only if they represent the same linear operator with respect to (possibly) different bases, similar matrices share all properties of their shared underlying operator: Rank; Characteristic polynomial, and attributes that can be derived from it:
In fluid mechanics, dynamic similarity is the phenomenon that when there are two geometrically similar vessels (same shape, different sizes) with the same boundary conditions (e.g., no-slip, center-line velocity) and the same Reynolds and Womersley numbers, then the fluid flows will be identical.
In data analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of the angle between the vectors; that is, it is the dot product of the vectors divided by the product of their lengths. It follows that the cosine similarity does not depend on the ...
The rule of similarity states that images that are similar to each other can be grouped together as being the same type of object or part of the same object. Therefore, the more similar two images or objects are, the more likely it will be that they can be grouped together. For example, two squares among many circles will be grouped together.
In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics : they take on large values for similar ...