Encyclopedia of Distances This 4 th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers as well a general streamlining of content and the addition of essential new topics. Though the structure remains unchanged the new edition also explores recent advances in the use of distances and metrics for e.g. generalized distances probability theory graph theory coding theory data analysis. New topics in the purely mathematical sections include e.g. the Vitanyi multiset metric algebraic point conic distance triangular ratio metric Rossi Hamming metric Taneja distance spectral semimetric between graphs channel metrization and Maryland bridge distance. The multidisciplinary sections have also been supplemented with new topics including: dynamic time wrapping distance memory distance allometry atmospheric depth elliptic orbit distance VLBI distance measurements the astronomical system of units and walkability distance. Leaving aside the practical questions that arise during the selection of a ‘good’ distance function this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances. As well as providing standalone introductions and definitions the encyclopedia facilitates swift cross referencing with easily navigable bold faced textual links to core entries. In addition to distances themselves the authors have collated numerous fascinating curiosities in their Who’s Who of metrics including distance related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non specialists justly view as arcane. In expanding access to these techniques and in many cases enriching the context of distances themselves this peerless volume is certain to stimulate fresh research. Part I. Mathematics of Distances: 1 General Definitions 2 Topological Spaces 3 Generalization of Metric Spaces 4 Metric Transforms 5 Metrics on Normed Structures Part II. Geometry and Distances: 6 Distances in Geometry 7 Riemannian and Hermitian Metrics 8 Distances on Surfaces and Knots 9 Distances on Convex Bodies Cones and Simplicial Complexes Part III. Distances in Classical Mathematics: 10 Distances in Algebra 11 Distances on Strings and Permutations 12 Distances on Numbers Polynomials and Matrices 13 Distances in Functional Analysis 14 Distances in Probability Theory Part IV. Distances in Applied Mathematics: 15 Distances in Graph Theory 16 Distances in Coding Theory 17 Distances and Similarities in Data Analysis 18 Distances in Systems and Mathematical Engineering Part V. Computer Related Distances: 19 Distances on Real and Digital Planes 20 Voronoi Diagram Distances 21 Image and Audio Distances 22 Distances in Networks Part VI. Distances in Natural Sciences: 23 Distances in Biology 24 Distances in Physics and Chemistry 25 Distances in Earth Science and Astronomy 26 Distances in Cosmology and Theory of Relativity Part VII. Real World Distances: 27 Length Measures and Scales 28 Distances in Applied Social Sciences 29 Other Distances.