Difference between revisions of "User:Foxjwill"
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For some curve <math>C</math> parametrized by <math>\mathbf{r}(t)</math>, the Frenet frame is defined as | For some curve <math>C</math> parametrized by <math>\mathbf{r}(t)</math>, the Frenet frame is defined as | ||
<math>W=\{u\hat{\mathbf{N}}+ v\hat{\mathbf{T}}: u,v \in \mathbb{R}\}</math>. The Curvy Area is then defined as | <math>W=\{u\hat{\mathbf{N}}+ v\hat{\mathbf{T}}: u,v \in \mathbb{R}\}</math>. The Curvy Area is then defined as | ||
| + | <cmath>\def\proj{\mathop{\rm proj}\nolimits} A = {\int_{t_1}^{t_2} {\int_{t_1}^{t_2}\left [ {\mathrm{proj}_{W(v)} \left( \mathbf{r}(u) | ||
| + | - \mathbf{r}(v) \right)\right ] du}dv}</cmath> | ||
| + | |||
<cmath>A = {\int_{t_1}^{t_2} {\int_{t_1}^{t_2}\left [ {\mathrm{proj}_{W(v)} \left( \mathbf{r}(u) | <cmath>A = {\int_{t_1}^{t_2} {\int_{t_1}^{t_2}\left [ {\mathrm{proj}_{W(v)} \left( \mathbf{r}(u) | ||
- \mathbf{r}(v) \right)\right ] du}dv}</cmath> | - \mathbf{r}(v) \right)\right ] du}dv}</cmath> | ||
Revision as of 19:07, 6 June 2008
Curvy Area
For some curve 
parametrized by 
, the Frenet frame is defined as
. The Curvy Area is then defined as
\[\def\proj{\mathop{\rm proj}\nolimits} A = {\int_{t_1}^{t_2} {\int_{t_1}^{t_2}\left [ {\mathrm{proj}_{W(v)} \left( \mathbf{r}(u)
- \mathbf{r}(v) \right)\right ] du}dv}\] (Error compiling LaTeX. Unknown error_msg)
\[A = {\int_{t_1}^{t_2} {\int_{t_1}^{t_2}\left [ {\mathrm{proj}_{W(v)} \left( \mathbf{r}(u)
- \mathbf{r}(v) \right)\right ] du}dv}\] (Error compiling LaTeX. Unknown error_msg)
limit test thingy
![\[\lim_{x\to a}f(x)\]](http://latex.artofproblemsolving.com/1/1/7/1171ff821a4b63cfcfe6d5c26ea0be52fd50965d.png)
\[\def\proj{\mathop{\rm proj}\nolimits} \proj_W x\] (Error compiling LaTeX. Unknown error_msg)
