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Yaglom - Google Books</title><link rel="stylesheet" href="/books/css/_a33f2a89320471e58c940b9287b9d4eb/kl_viewport_kennedy_full_bundle.css" type="text/css" /><link rel="stylesheet"href="https://fonts.googleapis.com/css2?family=Product+Sans:wght@400"><script src="/books/javascript/v2_a33f2a89320471e58c940b9287b9d4eb__en.js"></script><script>_OC_Hooks = ["_OC_Page", "_OC_SearchReload", "_OC_TocReload", "_OC_EmptyFunc", "_OC_SearchPage", "_OC_QuotePage" ];for (var _OC_i = 0; _OC_i < _OC_Hooks.length; _OC_i++) {eval("var " + _OC_Hooks[_OC_i] + ";");}function _OC_InitHooks () {for (var i = 0; i < _OC_Hooks.length; i++) {var func = arguments[i];eval( _OC_Hooks[i] + " = func;");}}</script><link rel="canonical" href="https://books.google.com/books/about/A_Simple_Non_Euclidean_Geometry_and_Its.html?id=FyToBwAAQBAJ"/><meta property="og:url" content="https://books.google.com/books/about/A_Simple_Non_Euclidean_Geometry_and_Its.html?id=FyToBwAAQBAJ"/><meta name="title" content="A Simple Non-Euclidean Geometry and Its Physical Basis"/><meta name="description" content="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. 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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.","my_library_url":"https://www.google.com/accounts/Login?service=print\u0026continue=https://books.google.com.sg/books%3Fop%3Dlibrary\u0026hl=en","is_magazine":false,"is_public_domain":false,"last_page":{"pid":"PA309","order":325,"title":"309"}},{"enableUserFeedbackUI":true,"pseudocontinuous":true,"is_cobrand":false,"sign_in_url":"https://www.google.com/accounts/Login?service=print\u0026continue=https://books.google.com.sg/books%3Fid%3DFyToBwAAQBAJ%26q%3Dscalar%2Bproduct%26source%3Dgbs_word_cloud_r%26hl%3Den\u0026hl=en","isEntityPageViewport":false,"showViewportOnboarding":false,"showViewportPlainTextOnboarding":false},{"page":[{"pid":"PA245","flags":8,"order":263,"vq":"scalar product"}]},null,{"number_of_results":8,"search_results":[{"page_id":"PA74","page_number":"74","snippet_text":"... \u003cb\u003escalar product\u003c/b\u003e of the doublets A ( § , ŋ ) and B ( §1,71 ) is equal to AB = \u0026amp; $ 1 . ( 26b ) Equation ( 26b ) shows that \u003cb\u003escalar multiplication\u003c/b\u003e of doublets satisfies axioms IV1 - IV ) : AB = BA , ( αA ) B = a ( AB ) , ( A + B ) C = AB +\u0026nbsp;..."},{"page_id":"PA75","page_number":"75","snippet_text":"... \u003cb\u003escalar product\u003c/b\u003e ab cd = 8ab 8cd , we can define the cross product ab × cd = 8ab 8cddpQ · If A = A ( § , n ) and B = B ( §1,71 ) , then it is easy to see that AxB = $ n - n ( 27 ) ( 27a ) Formula ( 27a ) implies the following relations\u0026nbsp;..."},{"page_id":"PA245","page_number":"245","snippet_text":"... \u003cb\u003escalar product\u003c/b\u003e of vectors , which associates to a pair of vectors a , b a number o called the \u003cb\u003escalar product\u003c/b\u003e of a and b and denoted by ab . The \u003cb\u003escalar product\u003c/b\u003e is governed by the following axioms . IV ( E ) . 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