Difference between revisions of "User:Foxjwill"
(New page: 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 C...) |
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| + | ==Curvy Area== | ||
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>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> | ||
| + | |||
| + | ==limit test thingy== | ||
| + | <cmath>\lim{x\to a}f(x)</cmath> | ||
Revision as of 20:03, 6 June 2008
Curvy Area
For some curve 
parametrized by 
, the Frenet frame is defined as
. The Curvy Area is then defined as
\[A = {\int_{t_1}^{t_2} {\int_{t_1}^{t_2}\left [ {\mathrm{proj}_{W(v)} \left( \mathbf{r}(u)
- \mathbf{r}(v) \right)\right ] du}dv}\] (Error compiling LaTeX. Unknown error_msg)
limit test thingy
![\[\lim{x\to a}f(x)\]](http://latex.artofproblemsolving.com/c/0/a/c0a27c2a908d3d6b0463e585a2112f1873bf228b.png)
