## Dictionary of DistancesThis book comes out of need and urgency (expressed especially in areas of Information Retrieval with respect to Image, Audio, Internet and Biology) to have a working tool to compare data. The book will provide powerful resource for all researchers using Mathematics as well as for mathematicians themselves. In the time when over-specialization and terminology fences isolate researchers, this Dictionary try to be "centripedal" and "oikoumeni", providing some access and altitude of vision but without taking the route of scientific vulgarisation. This attempted balance is the main philosophy of this Dictionary which defined its structure and style. Key features: - Unicity: it is the first book treating the basic notion of Distance in whole generality. - Interdisciplinarity: this Dictionary is larger in scope than majority of thematic dictionaries. - Encyclopedicity: while an Encyclopedia of Distances seems now too difficult to produce, this book (by its scope, short introductions and organization) provides the main material for it and for future tutorials on some parts of this material. - Applicability: the distances, as well as distance-related notions and paradigms, are provided in ready-to-use fashion. - Worthiness: the need and urgency for such dictionary was great in several huge areas, esp. Information Retrieval, Image Analysis, Speech Recognition and Biology. - Accessibility: the definitions are easy to locate by subject or, in Index, by alphabetic order; the introductions and definitions are reader-friendly and maximally independent one from another; still the text is structured, in the 3D HTML style, by hyperlink-like boldfaced references to similar definitions. * Covers a large range of subjects in pure and applied mathematics * Designed to be easily applied--the distances and distance-related notions and paradigms are ready to use * Helps users quickly locate definitions by subject or in alphabetical order; stand-alone entries include references to other entries and sources for further investigation |

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### Contents

Part II Geometry and Distances | 61 |

Part III Distances in Classical Mathematics | 133 |

Part IV Distances in Applied Mathematics | 189 |

Part V ComputerRelated Distances | 239 |

Part VI Distances in Natural Sciences | 287 |

Part VII RealWorld Distances | 341 |

371 | |

378 | |

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### Common terms and phrases

afﬁne angle Banach space binary celestial compact connected constant convex corresponding curvature curve deﬁned denotes dimension edge elliptic equal equivalent Euclidean distance Euclidean space example exists ﬁnite Finsler Finsler metric ﬁrst ﬁxed geodesic Geometry Given a metric graph G Hausdorff Hausdorff distance Hermitian Hermitian metric hyperbolic inequality inﬁnite inner product integer intrinsic metric isometric length line element line element ds2 linear manifold Mn mapping matrix measure metric Given metric Let metric space X,d metric tensor minimum number n-dimensional obtained operator pair parameter path metric plane Poincare metric positive projective metric quasi-distance radius real number respectively Riemannian metric scalar semi-metric sequence shortest similarity space-time sphere subgraph subset subspace surface symmetric tangent topological space transform tree triangle triangle inequality vector space vertex-set vertices Voronoi diagram Voronoi generation distance weighted