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Author: Juan Carlos Bustamante
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Section 8.1, n. 26

Juste le graphique pour voir, même si ce n'était pas demandé.

var('t,s') C = parametric_plot3d([sin(t), cos(t), (sin(t))^2], (t,0,2*pi), color= "blue", thickness = 4) # La courbe donnée Cyl = parametric_plot3d([cos(t), sin(t), s], (t,0,2*pi), (s, -1, 2), color="green", opacity = 0.25) # Le cylindre circulaire Cyl2 = parametric_plot3d([t,s,t^2],(t,-1,1),(s,-1.5,1.5), color="red", opacity = 0.25)#Le cylindre parabolique show(C+Cyl + Cyl2)
(t\displaystyle t, s\displaystyle s)
3D rendering not yet implemented

Section 8.3, n. 38

var('t') typeset_mode(True) x(t) = sin(3*t) y(t) = sin(2*t) z(t) = sin(3*t) Courbe = parametric_plot3d([x(t),y(t),z(t)],(t,0,2*pi), color= "blue", thickness= 3) show(Courbe)
t
3D rendering not yet implemented
r = vector([x(t),y(t),z(t)]) v = diff(r,t) a = diff(r,t,2)

On calcule la fonction de courbure avec la formule κ(t)=r(t)×r(t)r(t)3\kappa(t) =\frac{|\mathbf{r}'(t) \times \mathbf{r}''(t)|}{|\mathbf{r}'(t)|^3}

k(t) = (v.cross_product(a)).norm()/(v.norm())^3
Courbe = parametric_plot((t,k(t)),(t,0,2*pi),title='Fonction de courbure', axes_labels=['$t$','$\kappa (t)$'], ticks=pi/3,tick_formatter=pi,plot_points=600) show(Courbe, aspect_ratio = 0.1, figsize=12)