پديد آورنده :
شيخ بهايي، فاطمه
عنوان :
قانون جمع سرعت هاي نسبيتي اينشتين و هندسه ي هذلولوي
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي﴿هندسه﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
96ص.: مصور، جدول، نمودار
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
قهرمان طاهريان
استاد مشاور :
منصور آقاسي
توصيفگر ها :
نسبيت خاص , مثلثات هذلولوي , جاير وگروه , جاير و بردار
تاريخ نمايه سازي :
24/8/91
استاد داور :
بهروز ميرزا، اعظم اعتماد
تاريخ ورود اطلاعات :
1396/09/21
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Abstract Addition Law And It s Hyperbolic GeometryThe hyperbolic law of cosines is nearly a century old result that hassprung from the soil of Einstein velocity addition law that Einsteinintroduced in his 1905 paper 5 23 that founded the special theory ofrelativity It was established by Sommerfeld 1868 1951 in 1909 3 interms of hyperbolic trigonometric functions as a consequence ofEinstein s velocity addition of relativistically admissible velocities Soonafter Vari ak 1865 1942 established in 1912 68 the interpretation ofSommerfeld s consequence in the hyperbolic geometry of Bolyai andLobachevski Vari ak s interpretation marks the first uncovered linkbetween Einstein s velocity addition law and hyperbolic geometry This thesis is based on the works of two mathematicians Helmut Karzeland Abraham Ungar which open a new perspective and new way in therelation between hyperbolic geometry and special relativity Thisapproach had profound similarities with the conventional approach tovector space in Euclidean geometry These analogies allow us to utilizetheir knowledge of Euclidean geometry and Newtonian physics to gainof hyperbolic geometry and special relativity The gyrovectors that give rise to gyrovector spaces are hyperbolicvectors that allow Einstein s velocity addition to be presented asgyrovector addition In 1924 Vari ak had to admit to his chagrin that theadaption of vector algebra for use in hyperbolic space was just notfeasible 69 as noted by Walter in 73 Accordingly the introductionof vector algebra into hyperbolic geometry offered in 49 was noted byWalter in 74 In fact hyperbolic vectors that is gyrovectors arepresented in 48 as equivalence classes of directed hyperbolic segmentsthat add according to the hyperbolic parallelogram gyroparallelogram addition law just as vectors are equivalence classes of directed segmentsthat add according to the parallelogram addition law in Euclideangeometry
استاد راهنما :
قهرمان طاهريان
استاد مشاور :
منصور آقاسي
استاد داور :
بهروز ميرزا، اعظم اعتماد
