αναλυτικη γεωμετρια

  • Published on
    25-Nov-2015

  • View
    713

  • Download
    2

Embed Size (px)

Transcript

<ul><li><p> 2012 </p></li><li><p> . 1996 2004 2005 . . . . . . , . . . 32 . . . </p><p> , , . , . </p><p> 2012 </p></li><li><p> 5</p><p> ...................................................................................................................5</p><p>...........................................................................................................................1</p><p>...............................................................................................................................3</p><p>.....................................................................................................................31.1 ..................................................................................................................31.2 ...........................................................................................................51.3 ................................................................................................71.4 ,...............................................................121.5 ...............................................................................................12.....................................................................................................................................................20</p><p>.....................................................................................................................23</p><p>.....................................................................232.1.................................................................232.2 ........................................................................................................242.3 ..............................................................................252.4 .....................................................................................26..............................................................................................................................................28</p><p>....................................................................................................................31</p><p>.....................................................................................................................313.1 ........................................................................................................313.2 ............................................................................323.3 ........................................................................343.4 ............................................................................................................353.5 ............363.6. ......................................................................................................................393.7 ....................................................................................39Ax+By+0....................................................................................................393.8 ...................................................................................................40.....................................................................................................................................................42</p><p>IV....................................................................................................................43</p><p>...............................................................................................434.1 .....................................................................................................434.2 ......................................................454.3 Ax+By+z+=0.........................................................................................464.4 ................................................494.5 ...........................................................................................................504.6 .............................................................................................534.7 ......................................................................................................534.8 ....................................................................................................................54</p></li><li><p> 6</p><p>.....................................................................................................................................54......................................................................................................................544.9 ........................................................................................................564.10 ...........57.....................................................................................................................................................59</p><p>V....................................................................................................................61</p><p>...........................................615.1 ................................................................................................................................................615.2 .......................................................................625.3 .............................................................................................................................................645.4 .......................................................................655.5 ............................................................................................665.6 ...................................................675.7 ..........................................................................................................................................695.8 ..............................................................................................715.9 .........................................................................................725.10 ,.................................................................725.11 ................................................................................765.12 ....................................................................................................................................785.13 .........................................................................................805.14 ...................................................................................805.15 .............................................................................................81.....................................................................................................................................................82</p><p>V...................................................................................................................85</p><p>.........................................................................................856.1 ................................................................................................................................................856.2 ...........................................................................................866.3 ............................................................................................876.4 ..............................................................................................................89.....................................................................................................................................................92</p><p>VII..................................................................................................................95</p><p>.......................................................................................................957.1...................................................................................................................................................957.2,..................................................967.3 ...............................987.4 ............................................................99...................................................................................................................................................102</p><p>VIII................................................................................................................103</p><p>...........................................................................................................................1038.1 .........................................................................................................................................1038.2 ........................................................................................................................1038.3 ..................................................................................................................1058.4 ...........................................................................................................107...................................................................................................................................................119</p></li><li><p> 7</p><p>..................................................................................................................121</p><p>...............................................................1219.1 ..............................................................................................................................................1219.2 ...................................................................................................................1219.3 ...................................................................................................................1239.4 ...........................................................................................1249.5 ..................................................................................................................1259.6 .....................................................................1279.7 ,..........................................1289.8 ......................................................................................1309.9 SerretFrenet.............................................................................................1319.10 T......................................................................132...................................................................................................................................................135</p><p>...............................................................................................................137</p><p>................................................................................137</p><p>......................................................................................................137</p><p>................................................................................................................138</p><p>..........................................................................................................139</p><p>...........................................................................................139</p><p>IV................................................................................................140</p><p>V...............................................................................................141</p><p>B...............................................................................................................143</p><p>..............................................................................143...............................................................................................................143B.1 ....................................................................................................................143B.2 ........................................................................................................145B.3 ...............................................................................................147</p><p>1.......................................................................149</p><p>2.......................................................................155</p><p>3........................................................................158</p><p>4........................................................................161</p><p>5.......................................................................171</p><p>6.......................................................................179</p><p>7........................................................................187</p><p>8.......................................................................193</p><p>9........................................................................200</p><p>...........................................................................................................209</p></li><li><p> 8</p><p>....................................................................................213</p><p>......................................................................................................................233</p><p>................................................................................................................236</p></li><li><p> , ' ' . (1, (Descartes), 1637 (x,y,z), . , , . , .. , , ... , . x, y z , . , (2. (x,y,z) : F(x,y,z)=0 .. F(x,y,z)=x2+y2+z2-R2=0, , R. . F(x,y,z)=0 x, y, z : z=f(x,y) x=g(y,z) y=h(x,z) . .. , z : </p><p> 2 2 2z R x y= 2 2 2z R x y= </p><p> (1 RENE CARTESIUS (1596-1650). . , , , (La Geometrie 1637). O Cartesius, Fermat, . (2 , . , ... </p></li><li><p>2</p><p> . : F(x,y,z)=0 G(x,y,z)=0 . . OXY, z=0 f(x,y)=0. .. x2+y2=R2, z=0 , x2+y2+z2=R2 OXY, ( z=0). , . . , . . : , . . 1788 Lagrange(3 Mecanique Analytique, ( ), . . , , . </p><p> (3 JOSEPH LOUIS LAGRANCE (1736-1813), . 19 1766 . 1787 . , , , , , . </p></li><li><p>1.1 .</p><p> () , . () , . ( ), , (,). () (4. , , , ||. B : || B = (1) -|| (,). x . . (,) Ox. , .. OY, , 1 ....</p></li></ul>