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 aspecto mais triste da humanidade hoje
É que ela cresce mais em ciência do que em sabedoria.

Isaac Asimov

< Parabola | Ellipse | Hyperbola >

Ellipse

\[ \left( \frac{x}{a} \right)^2+\left( \frac{y}{b} \right)^2 =1 \]

Formulas

$\underline{\mathbf{r}}(t)=\left(\begin{array}{c} a \cos{t}\\ b \sin{t} \end{array}\right)+\underline{\mathbf{r}}_0$	$\underline{\mathbf{r}}'(t)=\left(\begin{array}{c} -a \sin{t}\\ b \cos{t} \end{array}\right)$
$\underline{\mathbf{r}}''(t)=\left(\begin{array}{c} -a \cos{t}\\ -b \sin{t} \end{array}\right)$	$\widehat{\underline{\mathbf{r}}}'(t)=-\left(\begin{array}{c} b \cos{t}\\ a \sin{t} \end{array}\right)$
$v(t)^2=a^2 \sin^2{t}+b^2 \cos^2{t}$	$D(t)=ab>0$
$\underline{\mathbf{t}}(t)= \frac{1}{ \sqrt{a^2 \sin^2{t}+b^2 \cos^2{t}} } \cdot \left(\begin{array}{c} -a \sin{t}\\ b \cos{t} \end{array}\right)$	$\underline{\mathbf{n}}(t)=\frac{-1}{ \sqrt{a^2 \sin^2{t}+b^2 \cos^2{t}} } \left(\begin{array}{c} b \cos{t}\\ a \sin{t} \end{array}\right)$
$\psi(t)=\frac{ab}{ a^2 \sin^2{t}+b^2 \cos^2{t} }$	$\varphi(t)=\frac{ a^2 \sin^2{t}+b^2 \cos^2{t} }{ab}$
$\kappa(t)=\frac{ab}{ (a^2 \sin^2{t}+b^2 \cos^2{t})^{3/2} }$	$\rho(t)=\frac{ (a^2 \sin^2{t}+b^2 \cos^2{t})^{3/2} }{ab}$
$\underline{\mathbf{c}}(t)=\frac{a^2-b^2}{ab} \left(\begin{array}{c} b \cos^3{t}\\ -a \sin^3{t} \end{array}\right)$
$\underline{\mathbf{c}}'(t)=-3\frac{a^2-b^2}{ab}\cos{t}\sin{t} \left(\begin{array}{c} b \cos{t}\\ a \sin{t} \end{array}\right)$
$\rho'(t)=3 \frac{a-b}{ab} \sqrt{a^2 \sin^2{t}+b^2 \cos^2{t}}\sin{t}\cos{t}$