Rayon de la base

A

B et C

Rayon de la base

D et E

Rayon de la base

F et G

Modifier le rayon de la base pour passer
du cas D au cas E tout en gardant un volume constant.

animation

Modifier le rayon de la base pour passer
du cas B au cas C tout en gardant un volume constant.

afficher la barre du temps

Modifier le rayon de la base pour passer
du cas F au cas G tout en gardant un volume constant.

temps = 9.45 (slider from 0 to 10, step 0.01)
A' = Point(yAxis)
a' = OrthogonalLine(A', yAxis)
G = Point(a')
base_{BC} = 0.32 (slider from 0.01 to 1.72, step 0.01)
haut_B: (-(base_{BC}) + sqrt(-3.0 * base_{BC}^(2.0) + 12.0)) / 2.0
para_B: 9.0 * base_{BC} / (haut_B - base_{BC})
bb = If(base_{BC} ≠ 1.0, (3.0 * 0.9 * 3.141592653589793 * x * para_B^(2.0) / (base_{BC}^(2.0) * 3.141592653589793) + para_B^(3.0))^(1.0 / 3.0) - para_B, 9.0 / 10.0 * x)
b = Function(bb, 0.0, 10.0)
D_1: (temps, b(temps))
B = Point(yAxis)
b' = OrthogonalLine(B, yAxis)
C = (1, 11)
c'_1 = OrthogonalLine(C, a')
D_2 = (3, 11)
d'_1 = OrthogonalLine(D_2, a')
E = Intersect(b', c'_1)
F = Intersect(b', d'_1)
H = Point(b')
e' = Segment(G, H)
I = (10, 9)
J = Intersect(xAxis, yAxis)
a = Function(9.0 / 10.0 * x, 0.0, 10.0)
A: (x(G), y(G) + a(temps))
b'' = OrthogonalLine(A, e')
K = Intersect(c'_1, b'')
L = Intersect(d'_1, b'')
f' = Segment(C, E)
g = Segment(D_2, F)
h = Segment(C, D_2)
A_1: (temps, 0.0)
A_2: (x(A_1), a(x(A_1)))
A_3: (0.0, y(A_2))
i = Segment(A_3, A_2)
j = Segment(A_2, A_1)
N = Point(a')
O = Point(a')
n_2 = OrthogonalLine(O, a')
q = OrthogonalLine(N, a')
o_1 = false
U = (2, 11)
r = OrthogonalLine(U, a')
V = Intersect(b', r)
s = Circle(U, base_{BC})
W = Intersect(s, a', 1.0)
Z = Intersect(s, a', 2.0)
t_4 = Circle(V, haut_B)
B_1 = Intersect(t_4, b', 2.0)
C_1 = Intersect(t_4, b', 1.0)
a_1 = Segment(C_1, W)
b_1 = Segment(Z, B_1)
E_1: (0.0, y(D_1))
e''_1 = Segment(E_1, D_1)
f'_2 = Segment(D_1, A_1)
H_B: (x(G), y(G) + y(D_1))
g_2 = OrthogonalLine(H_B, e')
F_1 = Intersect(g_2, a_1)
G_1 = Intersect(g_2, b_1)
polyB, n, f'_1, h_1, i_1 = Polygon(F_1, W, Z, G_1)
k_4 = Segment(O, N)
o = false
base_{DE} = 0.36 (slider from 0.2 to 1.4, step 0.01)
haut_D: sqrt(2.0 - base_{DE}^(2.0))
q_1 = Circle(V, haut_D)
r_4 = Circle(U, base_{DE})
D = Intersect(q_1, b', 1.0)
Q_1 = Intersect(q_1, b', 2.0)
R_1 = Intersect(r_4, a', 2.0)
S_1 = Intersect(r_4, a', 1.0)
s_3 = OrthogonalLine(Q_1, b')
t_1 = OrthogonalLine(D, b')
a_2 = OrthogonalLine(R_1, b')
b_2 = OrthogonalLine(S_1, a')
T_1 = (0, 15.5)
e''_2 = OrthogonalLine(T_1, yAxis)
U_1 = Intersect(t_1, e''_2)
V_1 = Intersect(b_2, e''_2)
W_1 = Intersect(a_2, e''_2)
Z_1 = Intersect(s_3, e''_2)
T1_D: 5.0 * base_{DE}^(2.0)
h_2: x = T1_D
C_2 = Intersect(h_2, i_3)
d_1(x) = y(C_2) / x(C_2) * x
d_5(x) = (y(I) - y(C_2)) / (x(I) - x(C_2)) * x - (y(I) - y(C_2)) / (x(I) - x(C_2)) * x(I) + y(I)
d = Function(If[x ≥ 0.0 ∧ x < T1_D, d_1, d_5], 0.0, 10.0)
E_2: (temps, d(temps))
F_2: (0.0, y(E_2))
c' = Segment(F_2, E_2)
k_6 = Segment(E_2, A_1)
B_2: (x(G), y(G) + y(E_2))
G_2 = Intersect(e''_2, e')
m_2 = OrthogonalLine(B_2, e')
I_2 = Intersect(t_1, m_2)
J_2 = Intersect(b_2, m_2)
K_2 = Intersect(a_2, m_2)
L_2 = Intersect(s_3, m_2)
l_4 = Segment(U_1, D)
r_3 = Segment(U_1, V_1)
i_4 = Segment(V_1, S_1)
p_3 = Segment(R_1, W_1)
q_3 = Segment(W_1, Z_1)
t_3 = Segment(Z_1, Q_1)
v = false
polyA, k, c_6, d_2, l = Polygon(K, C, D_2, L)
base_{FG} = 0.24 (slider from 0.06 to 1.7, step 0.01)
p_5 = Circle(U, base_{FG})
M = Intersect(p_5, a', 1.0)
P = Intersect(p_5, a', 2.0)
f_4 = Circle(V, base_{FG})
Q = Intersect(f_4, b', 1.0)
R = Intersect(f_4, b', 2.0)
S = (2, 15.5)
milieu_F: (-(base_{FG}) + sqrt(-3.0 * base_{FG}^(2.0) + 12.0)) / 2.0
g_4 = Circle(S, milieu_F)
T = Intersect(g_4, e''_2, 2.0)
E_3 = Intersect(g_4, e''_2, 1.0)
para_F: 9.0 * base_{FG} / (milieu_F - base_{FG})
f_1 = If(base_{FG} ≠ 1.0, Function[((3.0 * 0.9 * 3.141592653589793 * 2.0 * x * para_F^(2.0) / (base_{FG}^(2.0) * 3.141592653589793) + para_F^(3.0))^(1.0 / 3.0) - para_F) / 2.0, 0.0, 5.0], Function[9.0 / 10.0 * x, 0.0, 5.0])
f_2 = Function(-f_1(-(x) + 10.0) + 9.0, 5.0, 10.0)
f = Function(If[x ≥ 0.0 ∧ x ≤ 5.0, f_1, f_2], 0.0, 10.0)
G_3: (temps, f(temps))
H_3: (0.0, y(G_3))
f_3 = Segment(H_3, G_3)
m_4 = Segment(G_3, A_1)
I_3: (x(G), y(G) + y(G_3))
s_4 = OrthogonalLine(I_3, e')
polyF_1, c_3, d_3, g_3, h_3 = Polygon(T, P, M, E_3)
h_4 = Line(R, T)
n_4 = Line(Q, E_3)
q_4 = Line(M, E_3)
a_5 = Line(P, T)
J_3 = Intersect(s_4, q_4)
K_3 = Intersect(s_4, h_4)
L_3 = Intersect(s_4, n_4)
M_3 = Intersect(s_4, a_5)
polyF_3, k_3, t, e_3, l_3 = Polygon(K_3, T, E_3, L_3)
polyF_2, m, j_3, m_3, p_6 = Polygon(M, J_3, M_3, P)
p = false
n_5 = Segment(P, M)
q_5 = Segment(W, Z)
polyD_3, u_1, z_1, l_2, i_2 = Polygon(U_1, Z_1, L_2, I_2)
polyD_2, v_1, s_5, r_5, w_1 = Polygon(V_1, S_1, R_1, W_1)
polyD_1, j_2, s_1, r_1, k_2 = Polygon(J_2, S_1, R_1, K_2)
c = Segment(S_1, R_1)
e = Segment((0.0, 1.0), (10.0, 1.0))
c_1 = Segment((0.0, 2.0), (10.0, 2.0))
e_1 = Segment((0.0, 3.0), (10.0, 3.0))
g_1 = Segment((0.0, 4.0), (10.0, 4.0))
j_1 = Segment((0.0, 5.0), (10.0, 5.0))
k_1 = Segment((0.0, 6.0), (10.0, 6.0))
l_1 = Segment((0.0, 7.0), (10.0, 7.0))
m_1 = Segment((0.0, 8.0), (10.0, 8.0))
n_1 = Segment((0.0, 9.0), (10.0, 9.0))
p_1 = Segment((1.0, 0.0), (1.0, 9.0))
c_2 = Segment((2.0, 0.0), (2.0, 9.0))
e_2 = Segment((3.0, 0.0), (3.0, 9.0))
p_2 = Segment((4.0, 0.0), (4.0, 9.0))
q_2 = Segment((5.0, 0.0), (5.0, 9.0))
r_2 = Segment((6.0, 0.0), (6.0, 9.0))
s_2 = Segment((7.0, 0.0), (7.0, 9.0))
t_2 = Segment((8.0, 0.0), (8.0, 9.0))
a_3 = Segment((9.0, 0.0), (9.0, 9.0))
b_3 = Segment((10.0, 0.0), (10.0, 9.0))
u = true
anim = If(u ≟ true, 2.0, 0.0)
w = false
i_5 = Segment(T, P)
f_5 = Segment(M, E_3)
h_5 = Segment(T, R)
g_5 = Segment(E_3, Q)