CoCalc Public FilesDevoirs / D1.sagews
Author: Juan Carlos Bustamante
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Compute Environment: Ubuntu 18.04 (Deprecated)

## 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)

($\displaystyle t$, $\displaystyle s$)
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 $\kappa(t) =\frac{|\mathbf{r}'(t) \times \mathbf{r}''(t)|}{|\mathbf{r}'(t)|^3}$

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)