Mixing
relation between planes of a infinitesimal tetrahedron
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In relation to the tetrahedron depicted, the book I'm reading says that this relation between its surfaces holds:
$dsigma_i = dsigma_n cos(mathbf{n}, x_i) = n_i dsigma_m$
I don't understand how to derive it. If n is the unit exterior normal to the surface, (as the book defines it) then $n_i$ should be equal to 1, leading to $dsigma_i = 1cdot dsigma_m$
geometry trigonometry
asked Feb 3 at 9:12
Giuliano MalatestaGiuliano Malatesta
347
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add a comment |
$begingroup$
In relation to the tetrahedron depicted, the book I'm reading says that this relation between its surfaces holds:
$dsigma_i = dsigma_n cos(mathbf{n}, x_i) = n_i dsigma_m$
I don't understand how to derive it. If n is the unit exterior normal to the surface, (as the book defines it) then $n_i$ should be equal to 1, leading to $dsigma_i = 1cdot dsigma_m$
geometry trigonometry
asked Feb 3 at 9:12
Giuliano MalatestaGiuliano Malatesta
347
$endgroup$
$begingroup$
I think $n_i$ is the component of $mathbf{n}$ along axis $x_i$.
$endgroup$
– Aretino
Feb 3 at 10:56
add a comment |
$begingroup$
In relation to the tetrahedron depicted, the book I'm reading says that this relation between its surfaces holds:
$dsigma_i = dsigma_n cos(mathbf{n}, x_i) = n_i dsigma_m$
I don't understand how to derive it. If n is the unit exterior normal to the surface, (as the book defines it) then $n_i$ should be equal to 1, leading to $dsigma_i = 1cdot dsigma_m$
geometry trigonometry
asked Feb 3 at 9:12
Giuliano MalatestaGiuliano Malatesta
347
$endgroup$
In relation to the tetrahedron depicted, the book I'm reading says that this relation between its surfaces holds:
$dsigma_i = dsigma_n cos(mathbf{n}, x_i) = n_i dsigma_m$
I don't understand how to derive it. If n is the unit exterior normal to the surface, (as the book defines it) then $n_i$ should be equal to 1, leading to $dsigma_i = 1cdot dsigma_m$
geometry trigonometry
geometry trigonometry
asked Feb 3 at 9:12
Giuliano MalatestaGiuliano Malatesta
347
asked Feb 3 at 9:12
Giuliano MalatestaGiuliano Malatesta
347
edited Feb 3 at 9:20
Giuliano Malatesta
asked Feb 3 at 9:12
Giuliano MalatestaGiuliano Malatesta
347
asked Feb 3 at 9:12
Giuliano MalatestaGiuliano Malatesta
347
asked Feb 3 at 9:12
Giuliano MalatestaGiuliano Malatesta
347
347
$begingroup$
I think $n_i$ is the component of $mathbf{n}$ along axis $x_i$.
$endgroup$
– Aretino
Feb 3 at 10:56
add a comment |
$begingroup$
I think $n_i$ is the component of $mathbf{n}$ along axis $x_i$.
$endgroup$
– Aretino
Feb 3 at 10:56
$begingroup$
I think $n_i$ is the component of $mathbf{n}$ along axis $x_i$.
$endgroup$
– Aretino
Feb 3 at 10:56
$begingroup$
I think $n_i$ is the component of $mathbf{n}$ along axis $x_i$.
$endgroup$
– Aretino
Feb 3 at 10:56
add a comment |
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$begingroup$
I think $n_i$ is the component of $mathbf{n}$ along axis $x_i$.
$endgroup$
– Aretino
Feb 3 at 10:56