SmtC: Show me the Code!

SmtC: Show me the Code

Ole Peter Smith

Instituto de Matemática e Estatística

Universidade Federal de Goiás

http://www.olesmith.com.br

Cones

O dia que bosta valesse ouro.
Os pobres todos nascerão sem c*.

Grafitti.

< Ellipse | Hyperbola | Other Curves >

Hyperbola

$\left( \frac{x}{a} \right)^2-\left( \frac{y}{b} \right)^2$ =1

Formulas

$\underline{\mathbf{r}}(t)=\left(\begin{array}{c} a\sqrt{1+t^2}\\ bt \end{array}\right)$	$\underline{\mathbf{r}}'(t)=\left(\begin{array}{c} \frac{at}{\sqrt{1+t^2}}\\ b \end{array}\right)$
$\underline{\mathbf{r}}''(t)=\left(\begin{array}{c} a(1+t^2)^{-3/2}\\ 0 \end{array}\right)$	$\widehat{\underline{\mathbf{r}}}'(t)=-\left(\begin{array}{c} -b\\ \frac{at}{\sqrt{1+t^2}} \end{array}\right)$
$v(t)^2=\frac{ (a^2+b^2) t^2+b^2 }{ 1+t^2 }$	$D(t)=-ab (1+t^2)^{-3/2}$
$\underline{\mathbf{t}}(t)=\sqrt{\frac{ 1+t^2 }{ (a^2+b^2) t^2+b^2 }}\left(\begin{array}{c} \frac{at}{\sqrt{1+t^2}}\\ b \end{array}\right)$	$\underline{\mathbf{n}}(t)=\sqrt{\frac{ 1+t^2 }{ (a^2+b^2) t^2+b^2 }}\left(\begin{array}{c} -b\\ \frac{at}{\sqrt{1+t^2}} \end{array}\right)$
$\psi(t)=-\frac{1}{ab} \cdot \frac{ \sqrt{1+t^2} }{ (a^2+b^2) t^2+b^2 }$	$\varphi(t)=-ab\cdot \frac{ (a^2+b^2) t^2+b^2 }{ \sqrt{1+t^2} }$
$\kappa(t)=-ab\left(\frac{ab}{ (a^2+b^2) t^2+b^2}\right)^{3/2}(1+t^2)^{-3}$	$\rho(t)=\frac{ (\frac{ (a^2+b^2) t^2+b^2 }{ 1+t^2 })^{3/2} }{ab}$
$\underline{\mathbf{c}}(t)=\frac{a^2+b^2}{ab}\left(\begin{array}{c} b(1+t^2)^{3/2}\\ -at^3 \end{array}\right)$
$\underline{\mathbf{c}}'(t)=-3\frac{a^2+b^2}{ab}\left(\begin{array}{c} bt\sqrt{1+t^2}\\ -at^2 \end{array}\right)$