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Area Mathematics - General concepts and linear algebra / Geometry

IEV ref102-04-34

en
tangent plane
at a point of a surface, plane, if it exists, which contains all the tangents at this point to the curves of the surface passing through the point

Note 1 to entry: For a surface defined by r=f(u,v) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahkhacqGH9aqpca WHMbGaaiikaiaadwhacaGGSaGaaGjbVlaadAhacaGGPaaaaa@4148@ , where (u,v)U R 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaacIcacaWG1bGaai ilaiaadAhacaGGPaGaeyicI4CcLbuacaqGvbGccqGHgksZieqacaWF sbWaaWbaaSqabeaajugabiaabkdaaaaaaa@440F@ , the tangent plane at point r(u0, v0) is defined by the vectors ( f u ) u= u 0 v= v 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaabmaabaWaaSaaae aacqGHciITcaWHMbaabaGaeyOaIyRaamyDaaaaaiaawIcacaGLPaaa daWgaaWceaqabeaacaWG1bGaeyypa0JaamyDamaaBaaameaacaaIWa aabeaaaSqaaiaadAhacqGH9aqpcaWG2bWaaSbaaWqaaiaaicdaaeqa aaaaleqaaaaa@43AB@ and ( f v ) u= u 0 v= v 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaabmaabaWaaSaaae aacqGHciITcaWHMbaabaGaeyOaIyRaamODaaaaaiaawIcacaGLPaaa daWgaaWcbaqbaeqabiqaaaqaaiaadwhacqGH9aqpcaWG1bWaaSbaaW qaaiaaicdaaeqaaaWcbaGaamODaiabg2da9iaadAhadaWgaaadbaGa aGimaaqabaaaaaWcbeaaaaa@43B2@ if they are linearly independent.


fr
plan tangent, m
en un point d'une surface, plan, s'il existe, qui contient toutes les tangentes en ce point aux courbes de la surface passant par le point

Note 1 à l'article: Pour une surface définie par r=f(u,v) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahkhacqGH9aqpca WHMbGaaiikaiaadwhacaGGSaGaaGjbVlaadAhacaGGPaaaaa@4148@ , où (u,v)U R 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaacIcacaWG1bGaai ilaiaadAhacaGGPaGaeyicI4CcLbuacaqGvbGccqGHgksZieqacaWF sbWaaWbaaSqabeaajugabiaabkdaaaaaaa@440F@ , le plan tangent en r(u0, v0) est défini par les vecteurs ( f u ) u= u 0 v= v 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaabmaabaWaaSaaae aacqGHciITcaWHMbaabaGaeyOaIyRaamyDaaaaaiaawIcacaGLPaaa daWgaaWceaqabeaacaWG1bGaeyypa0JaamyDamaaBaaameaacaaIWa aabeaaaSqaaiaadAhacqGH9aqpcaWG2bWaaSbaaWqaaiaaicdaaeqa aaaaleqaaaaa@43AB@ et ( f v ) u= u 0 v= v 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaabmaabaWaaSaaae aacqGHciITcaWHMbaabaGaeyOaIyRaamODaaaaaiaawIcacaGLPaaa daWgaaWcbaqbaeqabiqaaaqaaiaadwhacqGH9aqpcaWG1bWaaSbaaW qaaiaaicdaaeqaaaWcbaGaamODaiabg2da9iaadAhadaWgaaadbaGa aGimaaqabaaaaaWcbeaaaaa@43B2@ s'ils sont linéairement indépendants.


de
Tangentialebene, f

es
plano tangente (a una superficie)

ja
接平面

pl
powierzchnia styczna

pt
plano tangente

sr
тангентна раван, ж јд

sv
tangentplan

zh
切平面

Publication date: 2008-08
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