Search results
Results from the WOW.Com Content Network
If a similarity has exactly one invariant point: a point that the similarity keeps unchanged, then this only point is called "center" of the similarity. On the first image below the title, on the left, one or another similarity shrinks a regular polygon into a concentric one , the vertices of which are each on a side of the previous polygon.
Rarely used in modern mathematics without a horizontal bar delimiting the width of its argument (see the next item). For example, √2. √ (radical symbol) 1. Denotes square root and is read as the square root of. For example, +. 2. With an integer greater than 2 as a left superscript, denotes an n th root.
Figure 1: The point O is an external homothetic center for the two triangles. The size of each figure is proportional to its distance from the homothetic center. In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contraction of one another.
The two triangles on the left are congruent. The third is similar to them. The last triangle is neither congruent nor similar to any of the others. Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles. The unchanged properties are called invariants.
The above-mentioned fixed point S is called homothetic center or center of similarity or center of similitude. The term, coined by French mathematician Michel Chasles, is derived from two Greek elements: the prefix homo-(όμο ' similar '}; and transl. grc – transl. thesis (Θέσις) ' position '). It describes the relationship between two ...
Similarity (geometry), the property of sharing the same shape; Matrix similarity, a relation between matrices; Similarity measure, a function that quantifies the similarity of two objects Cosine similarity, which uses the angle between vectors; String metric, also called string similarity; Semantic similarity, in computational linguistics
The Tversky index, named after Amos Tversky, [1] is an asymmetric similarity measure on sets that compares a variant to a prototype. The Tversky index can be seen as a generalization of the Sørensen–Dice coefficient and the Jaccard index. For sets X and Y the Tversky index is a number between 0 and 1 given by
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 magnitudes of the vectors, but only on their angle. The cosine similarity always belongs to the interval [,].