<span class="defn">Hlicode :</span> 

<center>\(\left \lbrace \begin{matrix}x&=&u\cos(v)\\
y&=&u\sin(v)\\
z&=&v
\end{matrix}\right .\)
</center> 
En coordonnes cylindriques  : \( r = u, z = ) \theta

\def{text data=u*cos(v),u*sin(v),v,-3,3,0,2*pi}
\def{text data1=\data[1]}
\def{text data2=\data[2]}
\def{text data3=\data[3]}
\def{text data4=\data[4]}
\def{text data5=\data[5]}
\def{text data6=\data[6]}
\def{text data7=\data[7]}
\def{text data8=\data[8]}
\def{text data9=\data[9]}
\def{text data10=\data[10]}
\def{text data11=\data[11]}
\def{text data12=\data[12]}
\def{text data13=\data[13]}

<div class="exercice">
\tool{module=tool/geometry/animtrace.fr&+cmd=new&+type=parametric3DS&+special_parm=noshow&+quality=4&+x1=\data1&+y1=\data2&+z1=\data3&+uleft=\data4&+uright=\data5&+vleft=\data6&vright=\data7&
+xleft=\data8&+xright=\data9&+yleft=\data10&+yright=\data11&+zleft=\data12&+zright=\data13}{
Trac}
</div>



<span class="defn">Tore : </span> 
<a name="tore">
<center>\(\left \lbrace \begin{matrix}
x&=&(A+a \cos(u))\cos(v)\\
y&=&(A+a \cos(u))\sin(v)\\
z&=&a \sin(u)
\end{matrix}\right .\)
</center> 
avec \(A ) et \(a) des constantes. 
En coordonnes cylindriques&nbsp;: 
<center>\(
r&=&A+a\cos(\varphi)
\)
</center> 


\def{integer a=randint(1..2)}
\def{integer A=randint(3..6)}
\def{text data=(\A+\a*cos(u))*cos(v), (\A+\a*cos(u))*sin(v),\a*sin(u),-0,2*pi,0,2*pi}
\def{text data1=\data[1]}
\def{text data2=\data[2]}
\def{text data3=\data[3]}
\def{text data4=\data[4]}
\def{text data5=\data[5]}
\def{text data6=\data[6]}
\def{text data7=\data[7]}
\def{text data8=\data[8]}
\def{text data9=\data[9]}
\def{text data10=\data[10]}
\def{text data11=\data[11]}
\def{text data12=\data[12]}
\def{text data13=\data[13]}

<div class="exercice">\reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width="20" height="20">}{tore}
\tool{module=tool/geometry/animtrace.fr&+cmd=new&+type=parametric3DS&+special_parm=noshow&+quality=4&+x1=\data1&+y1=\data2&+z1=\data3&+uleft=\data4&+uright=\data5&+vleft=\data6&vright=\data7&
+xleft=\data8&+xright=\data9&+yleft=\data10&+yright=\data11&+zleft=\data12&+zright=\data13}{
Trac}
</div>

<span class="defn">Surface d'Enneper : </span>

<center>\(\left \lbrace \begin{matrix}
x&=&u-u^3/3+uv^2\\
y&=&v-v^3/3+vu^2\\
z&=&u^2-v^2
\end{matrix}\right .\)
</center>

\def{text data=u-u^3/3+u*v^2, v-v^3/3+v*u^2,u^2-v^2,-4,4,-4,4}
\def{text data1=\data[1]}
\def{text data2=\data[2]}
\def{text data3=\data[3]}
\def{text data4=\data[4]}
\def{text data5=\data[5]}
\def{text data6=\data[6]}
\def{text data7=\data[7]}
\def{text data8=\data[8]}
\def{text data9=\data[9]}
\def{text data10=\data[10]}
\def{text data11=\data[11]}
\def{text data12=\data[12]}
\def{text data13=\data[13]}

<div class="exercice">
\tool{module=tool/geometry/animtrace.fr&+cmd=new&+type=parametric3DS&+special_parm=noshow&+quality=4&+x1=\data1&+y1=\data2&+z1=\data3&+uleft=\data4&+uright=\data5&+vleft=\data6&vright=\data7&
+xleft=\data8&+xright=\data9&+yleft=\data10&+yright=\data11&+zleft=\data12&+zright=\data13}{
Trac}
</div>


<span class="defn"> Sans nom : </span>
<a name="sansnom">
<center>\(\left \lbrace \begin{matrix}x&=&\cos(u)\cos(v)(1+\sin(6v)\sin(5u)/5)\\
y&=&\cos(u)\sin(v)(1+\sin(6v)\sin(5u)/5)\\
z&=&\sin(u)(1+\sin(6v)\sin(5u)/5)\end{matrix}\right .\)
</center>
Cette surface a comme quation en coordonnes sphriques \((r,\theta,\varphi)) 
<center>  \(r=(1+\sin(6\theta)\sin(5 \varphi)/5)) </center>

\def{integer a=randint(2..5)}
\def{integer b=randint(2..8)}
\def{text data=cos(u)*cos(v)(1+sin(\b*v)*sin(\a*u)/\a),cos(u)*sin(v)(1+sin(\b*v)*sin(\a*u)/\a),sin(u)*(1+sin(\b*v)*sin(\a*u)/\a), 0,2*pi,0,2*pi}

\def{text data1=\data[1]}
\def{text data2=\data[2]}
\def{text data3=\data[3]}
\def{text data4=\data[4]}
\def{text data5=\data[5]}
\def{text data6=\data[6]}
\def{text data7=\data[7]}
\def{text data8=\data[8]}
\def{text data9=\data[9]}
\def{text data10=\data[10]}
\def{text data11=\data[11]}
\def{text data12=\data[12]}
\def{text data13=\data[13]}

<div class="exercice">\reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width="20" height="20">}{sansnom}
\tool{module=tool/geometry/animtrace.fr&+cmd=new&+type=parametric3DS&+special_parm=noshow&+quality=4&+x1=\data1&+y1=\data2&+z1=\data3&+uleft=\data4&+uright=\data5&+vleft=\data6&vright=\data7&
+xleft=\data8&+xright=\data9&+yleft=\data10&+yright=\data11&+zleft=\data12&+zright=\data13}{
Trac}
 pour \(x = cos(u)*cos(v)*(1+sin(\b*v)*sin(\a*u)/\a) , y =
 cos(u)*sin(v)*(1+sin(\b*v)*sin(\a*u)/\a), z = 
sin(u)*(1+sin(\b*v)*sin(\a*u)/\a)).
</div>