2016/07/23 by Vitor Balestro, Ákos G. Horváth, Balestro, Vitor +5 · 1 citation
Engineering · Mathematics · #46B20 #46C15 #46C50 #51M05 #51M25 #Advanced Numerical Analysis Techniques #Algebra over a field #Computer science #Euclidean geometry #Euclidean space #FOS: Mathematics #Field (mathematics) #Functional Analysis (math.FA) #Geometry #Mathematical proof #Mathematics #Measure (data warehouse) #Metric Geometry (math.MG) #Minkowski space #Orthogonality #Point processes and geometric inequalities #Primary: 52A21 Secondary: 32A70 #Pure mathematics #Space (punctuation) #Topology Optimization in Engineering #Variety (cybernetics) #math.FA #math.MG #msc:32A70 #msc:46B20 #msc:46C15 #msc:46C50 #msc:51M05 #msc:51M25 #msc:52A21
paper · pdf · doi:10.48550/arxiv.1607.06938
published in arXiv (Cornell University) (Cornell University) · 37 pages
arxiv created 2016/07/23 · openalex publication_date 2016/07/23 · arxiv updated 2016/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of angle, angle functions, and the question how to measure angles present old and well-established mathematical topics referring to Euclidean space, and there exist also various extensions to non-Euclidean spaces of different types. In particular, it is very interesting to investigate or to combine (geometric) properties of possible concepts of angle functions and angle measures in finite-dimensional real Banach spaces (= Minkowski spaces). However, going into this direction one will observe that there is no monograph or survey reflecting the complete picture of the existing literature on such concepts in a satisfying manner. We try to close this gap. In this expository paper (containing also new results, and new proofs of known results) the reader will get a comprehensive overview of this field, including also further related aspects. For example, angular bisectors, their applications, and angle types which preserve certain kinds of orthogonality are discussed. The latter aspect yields, of course, an interesting link to the large variety of orthogonality types in such spaces.