Suites arithmético-géométriques
Author: Yvan Monka - m@ths et tiques 2013

u_1

u_2

u_3

u_4

u_6

u_5

u_7

u_8

u_9

ord = 0
u_o = -2 (slider from -20 to 20, step 0.1)
a = 0.7 (slider from -10 to 10, step 0.1)
b = 2.8 (slider from -10 to 10, step 0.1)
f(x) = a * x + b
u_0: (u_o, ord)
d = Line(u_0, yAxis)
B = Intersect(f, d)
e = Line(B, xAxis)
C = Intersect(g, e)
h = Line(C, yAxis)
D = Intersect(f, h)
i = Line(D, xAxis)
E = Intersect(g, i)
j = Line(E, yAxis)
F = Intersect(f, j)
k = Line(F, xAxis)
G = Intersect(g, k)
l = Line(G, yAxis)
H = Intersect(f, l)
m = Line(H, xAxis)
I = Intersect(g, m)
n = Line(I, yAxis)
J = Intersect(f, n)
p = Line(J, xAxis)
K = Intersect(g, p)
q = Line(K, yAxis)
L = Intersect(f, q)
r = Line(L, xAxis)
M = Intersect(g, r)
N = Intersect(-(x(g) / y(g)) * x - z(g) / y(g), r, 1)
s = Line(M, yAxis)
O_2 = Intersect(f, s)
t = Line(O_2, xAxis)
P = Intersect(g, t)
a_1 = Line(P, yAxis)
Q = Intersect(f, a_1)
b_1 = Line(Q, xAxis)
R = Intersect(g, b_1)
c_1 = Line(R, yAxis)
S = Intersect(f, c_1)
d_1 = Line(S, xAxis)
T = Intersect(g, d_1)
e_1 = Line(T, yAxis)
U = Intersect(f, e_1)
f_1 = Segment(u_0, B)
g_1 = Segment(B, C)
h_1 = Segment(C, D)
i_1 = Segment(D, E)
j_1 = Segment(E, F)
k_1 = Segment(F, G)
l_1 = Segment(G, H)
m_1 = Segment(H, I)
n_1 = Segment(I, J)
p_1 = Segment(J, K)
q_1 = Segment(K, L)
r_1 = Segment(L, M)
s_1 = Segment(N, O_2)
t_1 = Segment(O_2, P)
a_2 = Segment(P, Q)
b_2 = Segment(Q, R)
c_2 = Segment(R, S)
d_2 = Segment(S, T)
e_2 = Segment(T, U)
f_2 = Line(U, d_2)
V = Intersect(g, f_2)
g_2 = Line(V, e_2)
W = Intersect(f, g_2)
h_2 = Line(W, d_2)
Y = Intersect(g, h_2)
i_2 = Line(Y, l_1)
Z_2 = Intersect(f, i_2)
j_2 = Line(Z_2, h_2)
A_1 = Intersect(g, j_2)
k_2 = Line(A_1, g_2)
B_1 = Intersect(f, k_2)
l_2 = Line(B_1, h_2)
C_1 = Intersect(g, l_2)
m_2 = Line(C_1, i_2)
D_1 = Intersect(f, m_2)
n_2 = Line(D_1, j_2)
E_1 = Intersect(g, n_2)
p_2 = Line(E_1, k_2)
F_1 = Intersect(f, p_2)
q_2 = Line(F_1, l_2)
G_1 = Intersect(g, q_2)
r_2 = Line(G_1, m_2)
H_1 = Intersect(f, r_2)
s_2 = Line(H_1, q_2)
I_1 = Intersect(g, s_2)
t_2 = Line(I_1, p_2)
J_1 = Intersect(f, t_2)
a_3 = Segment(U, V)
b_3 = Segment(V, W)
c_3 = Segment(W, Y)
d_3 = Segment(Y, Z_2)
e_3 = Segment(Z_2, A_1)
f_3 = Segment(A_1, B_1)
g_3 = Segment(B_1, C_1)
h_3 = Segment(C_1, D_1)
i_3 = Segment(D_1, E_1)
j_3 = Segment(E_1, F_1)
k_3 = Segment(F_1, G_1)
l_3 = Segment(G_1, H_1)
m_3 = Segment(H_1, I_1)
n_3 = Segment(I_1, J_1)
Z = Point(xAxis)
A = Intersect(-(x(g) / y(g)) * x - z(g) / y(g), f_1, 1)
K_1 = (9.899467021033377, -0.1330589849108391)
L_1 = (9.85833369055784, -0.910836762688617)
M_1 = (15.55529996141975, -0.9775034293552837)
E_2 = (15.473033300468677, -0.08861454046639464)
F_2 = (9.364733724851392, 0.24471879286693876)
G_2 = (9.364733724851392, -0.48861454046639474)
I_2 = (9.940600351508914, 0.3113854595336054)
s_4 = Segment(u_0, A)
T1: "u_{n+1} = " + a + " u_{n} + " + b + ""
c = OrthogonalLine(C, xAxis)
p_3 = OrthogonalLine(E, xAxis)
q_3 = OrthogonalLine(G, xAxis)
r_3 = OrthogonalLine(I, xAxis)
s_3 = OrthogonalLine(K, xAxis)
t_3 = OrthogonalLine(K, xAxis)
a_4 = OrthogonalLine(K, xAxis)
b_4 = OrthogonalLine(K, xAxis)
c_4 = OrthogonalLine(K, xAxis)
d_4 = OrthogonalLine(M, xAxis)
e_4 = OrthogonalLine(P, xAxis)
f_4 = OrthogonalLine(R, xAxis)
g_4 = OrthogonalLine(T, xAxis)
h_4 = OrthogonalLine(V, xAxis)
i_4 = OrthogonalLine(Y, xAxis)
j_4 = OrthogonalLine(A_1, xAxis)
O = Intersect(c, xAxis)
N_1 = Intersect(p_3, xAxis)
O_1 = Intersect(q_3, xAxis)
P_1 = Intersect(r_3, xAxis)
R_1 = Intersect(d_4, xAxis)
Q_1 = Intersect(s_3, t_3)
S_1 = Intersect(xAxis, s_3)
T_1 = Intersect(e_4, xAxis)
U_1 = Intersect(xAxis, f_4)
V_1 = Intersect(g_4, xAxis)
k_4 = Segment(C, O)
l_4 = Segment(N_1, E)
m_4 = Segment(O_1, G)
n_4 = Segment(P_1, I)
p_4 = Segment(K, S_1)
q_4 = Segment(R_1, M)
r_4 = Segment(P, T_1)
t_4 = Segment(U_1, R)
a_5 = Segment(T, V_1)