Minkowski Geometry—Some Concepts and Recent Developments

Balestro, Vitor; Martini, Horst

doi:10.1007/978-3-030-86695-2_3

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2024

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Cited by 3 publications

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“…The concept of Euclidean distance can be generalized to any linear space by the introduction of a norm. In this sense, the geometry that reveals with the help of norms in finite-dimensional Banach spaces is called Minkowski geometry (we refer the reader to [11][12][13] for a wider treatment). This is often confused with spacetime geometry, also called Minkowski geometry.…”

Section: Introductionmentioning

confidence: 99%

A New Approach for the Circular Inversion in l1- Normed Spaces

Ermiş,

Şen,

Gielis

2024

Preprint

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While there are well-known synthetic methods in the literature to find the image of a point under circular inversion in l2−normed geometry (Euclidean geometry), there is no similar synthetic method in Minkowski geometry, also known as the geometry of finite-dimensional Banach spaces. In this study, we have succeeded in giving a synthetic construction for the circular inversion in l1−normed spaces, which is one of the most fundamental examples of Minkowski geometry. Moreover, this synthetic construction has been given using the Euclidean circle, independently of the l1−norm.

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Section: Introductionmentioning

confidence: 99%