4533

4267

كارشناسي ارشد

رياضي محض﴿هندسه﴾

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1387

[هشت] ، 77، ص.: نمودار.

ص .ع. به :فارسي وانگليسي

قهرمان طاهريان

اعظم اعتماد

فارسي به انگليسي و انگليسي به فارسي

10/4/88

محمد مهدي ابراهيمي، منصور آقاسي

1396/09/12

كتابنامه

رياضي

ID4267

به فارسي وانگليسي: قابل رويت در نسخه ديجيتال

Introduction of Measures for Segments and Angles in a General Absolute Plane Elham Yavari yavari@math iut ac ir February 11 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr sayed ghahraman taherian taherian@cc iut ac ir2000 MSC Primary 51F05 Secondary 20N05Key words Absolute plane Distance function Measure of angles Group Loop Abstract In this thesis we present an expanded account of measure for segments and angles in ageneral absolute plane based on an article by Helmut Karzel 2007 Let o e1 e2 be a frameof reference of an absolute plane E L W o e1 the line joining the points o ande1 W the hal ine and E1 x E x o e1 o the unit circle with center o e1o and passing through e1 For a b E with a b let a b resp a b be the re ection inthe midpoint resp in the midline of the points a and b and a b the proper motion uniquelydetermined by a b a o and a b b W If a E L L let a resp L be the re ectionin the point a resp in the line L Then E with a b o a o b is a K loop W acommutative subgroup of E and W a positive domain of W hence W with a b b a W an ordered group Moreover there is an absolute value E W o x x o x x if x o and o osuch that E E W o x y x y x y is a distance describing the congruence and satisfying the triangular inequality such that a b a c c b c a b a b denotes the segment between a and b For each a E1 let a e1 a W if a e1 andlet e1 id Then E1 with a b a b is a commutative group isomorphic to each rotationgroup xing a point By setting x y z e1 x 1 z e1 e2 x 1 y for x y z E1 that 3 E x y z E x y z 3 and E x y z E 3 x y z E E1 3 3 3becomes a cyclic ordered group Let a b c and d e f be angles then theoriented measure of will be an element of the cyclic ordered group E1 given by o b a c E1 If b c e d then and can be added a b f isthe sum and for the oriented measures we have Moreover and are congruent if and only if 1 Finally we remark that E1 x x E1 is a commutative subgroup of the group M of all proper motions that for each a E a o a o is a proper motion and that foreach M there is exactly one pair a s E E1 such that a s Moreoverif a s b t E E1 then a s b t a s b a s b s t with 1 a b a b a b E1 That means that M E Q E1 is the quasidirectproduct of the K loop E and the commutative group E1 1

قهرمان طاهريان

اعظم اعتماد

محمد مهدي ابراهيمي، منصور آقاسي