podobnosti

Podobnosti (podobnost, plural: podobnosti) is a term used in mathematics and related fields to describe the degree to which two or more objects resemble each other. It denotes a qualitative or quantitative relation rather than exact identity, allowing comparison across shapes, data, or objects. The concept appears in geometry, statistics, computer science, linguistics, and information retrieval, where different measures of similarity are applied depending on the context.

In geometry, two figures are similar if there exists a similarity transformation that maps one onto the other. Such transformations combine scaling (dilation) with rigid motions like translation and rotation and preserve angle measures while changing size. Similarity is often described by a constant scale factor, the ratio of corresponding lengths, which implies proportionality of all corresponding sides and equality of corresponding angles. Similar triangles are the classic example, providing a way to deduce unknown lengths from known ones.

In data analysis and computer science, similarity is quantified by numerical similarity measures. Common examples include cosine similarity, Jaccard index, Dice coefficient, and Pearson correlation. These measures transform observed closeness into a value, typically between 0 and 1, and are fundamental in clustering, nearest-neighbor retrieval, recommender systems, and pattern recognition. Distance measures (e.g., Euclidean, Manhattan) can be converted into similarity scores, highlighting the close relationship between the two concepts.

Applications of podobnosti span many domains: comparing texts by string similarity, assessing image resemblance, or evaluating how closely experimental results align with models. The choice of measure depends on data type, desired properties, and the specific task.

See also: similarity, proportionality, transformation.