پديد آورنده :
رضايي تودشكي، عليرضا
عنوان :
فرمول هاي حجم در هندسه ي هذلولوي
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
هفت،91ص.نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
قهرمان طاهريان
استاد مشاور :
اعظم اعتماد دهكردي
تاريخ نمايه سازي :
8/11/92
استاد داور :
مجتبي آقايي فروشاني، امير هاشمي
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Formulas on hyperbolic volume Ali Reza Rezaei Toudeshki alireza rezaei@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Sayed Ghahreman Taherian taherian@cc iut ac ir Advisor Dr Azam Etemad Dehkordy ae110mat@ cc iut ac ir 2010 MSC 05C15 53C42 Keywords hyperbolic volume Lobachevsky function orthoscheme AbstractIn this dissertation we collects some important formulas on hyperbolic volume To determine concretevalues of the volume function of polyhedra is a very hard question requiring the knowledge of variousmethods Our goal is to give in 3 3 Theorem 2 3 3 a new non elementary integral on the volumeof the orthoscheme to obtain it without the Lobachevsky Schl i di erential formula using edge lengths as the only parameters At rst we recall concepts and preliminaries from foundations ofhyperbolic geometry Then we give certain formulas to some important coordinate systems andmodels respectively Afterwareds we collect the classical results on the three dimensional hyperbolicvolume of Bolyai and Lobachevsky The most famous volume integral depending on the dihedralangles of the orthosceme discovered by Lobachevsky is known and investigated worldwide howeverit is not well known that Bolyai also gave two formulas He used as parameters the measure of both thedihedral angles and the edges respectively There is no volume formula by edge lengths as parameters So as an application of some general formulas we compute such an integral Theorem 2 3 3 We willuse for this calculation the system of hyperbolic orthogonal coordinates Finally we give a collectionof some new interesting volume formulas of bodies discovered by contemporary mathematics showingthat this old and hard problem is evergreen In hyperbolic geometry we have a good chance to get aconcrete value of the volume function if we can transform our problem into either a suitable coordinatesystem or an adequate model of the space respectively In our computation we also use the distanceparameter used by Bolyai expressing the curvature K 2 of the hyperbolic space in the modern 1terminology
استاد راهنما :
قهرمان طاهريان
استاد مشاور :
اعظم اعتماد دهكردي
استاد داور :
مجتبي آقايي فروشاني، امير هاشمي
