Total Angle around a Point in Minkowski Plane

Dekster, B. V.

doi:10.1007/s00022-009-1919-9

Cited by 2 publications

(2 citation statements)

References 4 publications

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“…In this direction we can find papers of P. M. Miličič [64], C. R. Diminnie, E. Z. Andalafte, R. W. Freese [25,26] or H. Gunawan, J. Lindiarni, and O. Neswan [44]. Further related papers on angle measures are [22], [23], [24], [48] [37] and [38]. It is our aim to survey such concepts.…”

Section: Historymentioning

confidence: 99%

Angles in normed spaces

et al. 2016

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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.

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Section: Historymentioning

confidence: 99%

Angles in normed spaces

et al. 2016

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“…In this direction we can find also papers of P. M. Miličič [37], C. R. Diminnie, E. Z. Andalafte, R. W. Freese [10] or H. Gunawan, J. Lindiarni and O. Neswan [22]. Further related papers on angle measures are [7], [8], [9], and [26].…”

Section: Angle Measuresmentioning

confidence: 83%

Angle measures, general rotations, and roulettes in normed planes

2016

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In this paper a special group of bijective maps of a normed plane, called the group of general rotations, is introduced; it contains the isometry group as a subgroup. The concept of general rotations leads to the notion of flexible motions of the plane, and to the concept of Minkowskian roulettes. As a nice consequence of this new approach to motions the validity of a strong analogue to the Euler-Savary equations for Minkowskian roulettes is proved.

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Total Angle around a Point in Minkowski Plane

Cited by 2 publications

References 4 publications

Angles in normed spaces

Angles in normed spaces

Angle measures, general rotations, and roulettes in normed planes

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