LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	516
Title	A Simple Non-Euclidean Geometry and Its Physical Basis ([EBook] :) : An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity / / edited by Basil Gordon.
Added Personal Name	Gordon, Basil editor.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer New York, , 1979.
Physical Details	307 p. : online resource.
Series	Heidelberg science library 0073-1595
ISBN	9781461261353
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-6135-3
Links to Related Works	Subject References: Geometry . Mathematics . Authors: Gordon, Basil . Corporate Authors: SpringerLink (Online service) . Series: Heidelberg science library . Classification: 516 .

Catalogue Display

A Simple Non-Euclidean Geometry and Its Physical Basis: An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity /

Reviews