Titlebook: Circles, Spheres and Spherical Geometry; Hiroshi Maehara,Horst Martini Textbook 2024 The Editor(s) (if applicable) and The Author(s), unde

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Graphs and Circle-Systems,er first the orthogonal-circle representation (abbreviated as OCR) of a special type of graphs, called quadrangulations. An OCR of a graph is a circle-system consisting of circles each corresponding to a vertex of the graph, in which each pair of circles corresponding to a pair of adjacent vertices

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Quartets on a Sphere,proved by showing that any given region on a sphere contains a quartet (i.e., a four-point space) that is not isometrically embeddable in the plane. Actually, any region on a sphere contains a quartet whose six distances determine the radius of the sphere uniquely. Moreover, we present an equation t

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978-3-031-62778-1The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Hiroshi Maehara,Horst MartiniPresents cross-connections of geometry of circles and spherical geometry from various points of view.Motivates readers to derive own new results.Includes solutions to selected exercises

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