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Cover: 9780387903323 | A Simple Non-Euclidean Geometry and Its Physical Basis | I. M. Yaglom
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A Simple Non-Euclidean Geometry and Its Physical Basis
An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity
Taschenbuch von I. M. Yaglom
Sprache: Englisch

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Beschreibung
There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec­ tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.
There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec­ tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.
Inhaltsverzeichnis
1. What is geometry?.- 2. What is mechanics?.- I. Distance and Angle; Triangles and Quadrilaterals.- 3. Distance between points and angle between lines.- 4. The triangle.- 5. Principle of duality; coparallelograms and cotrapezoids.- 6. Proof s of the principle of duality.- II. Circles and Cycles.- 7. Definition of a cycle; radius and curvature.- 8. Cyclic rotation; diameters of a cycle.- 9. The circumcycle and incycle of a triangle.- 10. Power of a point with respect to a circle or cycle; inversion.- Conclusion.- 11. Einstein's principle of relativity and Lorentz transformations.- 12. Minkowskian geometry.- 13. Galilean geometry as a limiting case of Euclidean and Minkowskian geometry.- Supplement A. Nine plane geometries.- Supplement B. Axiomatic characterization of the nine plane geometries.- Supplement C. Analytic models of the nine plane geometries.- Answers and Hints to Problems and Exercises.- Index of Names.- Index of Subjects.
Details
Erscheinungsjahr: 1979
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Heidelberg Science Library
Inhalt: 307 S.
ISBN-13: 9780387903323
ISBN-10: 0387903321
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Yaglom, I. M.
Übersetzung: Shenitzer, A.
Auflage: Softcover reprint of the original 1st ed. 1979
Hersteller: Springer New York
Springer US, New York, N.Y.
Heidelberg Science Library
Maße: 235 x 155 x 19 mm
Von/Mit: I. M. Yaglom
Erscheinungsdatum: 28.02.1979
Gewicht: 0,505 kg
Artikel-ID: 107102267
Inhaltsverzeichnis
1. What is geometry?.- 2. What is mechanics?.- I. Distance and Angle; Triangles and Quadrilaterals.- 3. Distance between points and angle between lines.- 4. The triangle.- 5. Principle of duality; coparallelograms and cotrapezoids.- 6. Proof s of the principle of duality.- II. Circles and Cycles.- 7. Definition of a cycle; radius and curvature.- 8. Cyclic rotation; diameters of a cycle.- 9. The circumcycle and incycle of a triangle.- 10. Power of a point with respect to a circle or cycle; inversion.- Conclusion.- 11. Einstein's principle of relativity and Lorentz transformations.- 12. Minkowskian geometry.- 13. Galilean geometry as a limiting case of Euclidean and Minkowskian geometry.- Supplement A. Nine plane geometries.- Supplement B. Axiomatic characterization of the nine plane geometries.- Supplement C. Analytic models of the nine plane geometries.- Answers and Hints to Problems and Exercises.- Index of Names.- Index of Subjects.
Details
Erscheinungsjahr: 1979
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Heidelberg Science Library
Inhalt: 307 S.
ISBN-13: 9780387903323
ISBN-10: 0387903321
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Yaglom, I. M.
Übersetzung: Shenitzer, A.
Auflage: Softcover reprint of the original 1st ed. 1979
Hersteller: Springer New York
Springer US, New York, N.Y.
Heidelberg Science Library
Maße: 235 x 155 x 19 mm
Von/Mit: I. M. Yaglom
Erscheinungsdatum: 28.02.1979
Gewicht: 0,505 kg
Artikel-ID: 107102267
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