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IEVref:102-04-34ID:
Language:enStatus: Standard
Term: tangent plane
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Definition: 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.


Publication date:2008-08
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Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
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