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

u_1_6

u_1_5

u_1_4

u_1_3

u_1_2

u_1_1

u_1_0

u_9

u_8

u_7

u_6

u_5

u_4

u_3

u_2

u_1

ord = 0
u_o = -3 (slider from -20 to 20, step 0.1)
a = 1 (slider from -1.5 to 1.5, step 0.1)
r = 2.1 (slider from -10 to 10, step 0.1)
u_0: (u_o, ord)
f(x) = x + r
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_5 = Line(L, xAxis)
M = Intersect(g, r_5)
N = Intersect(-(x(g) / y(g)) * x - z(g) / y(g), r_5, 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 = (9.379467021033378, -0.373058984910839)
L_1 = (9.33833369055784, -1.1508367626886171)
M_1 = (15.035299961419751, -1.2175034293552836)
E_2 = (14.953033300468677, -0.3286145404663946)
F_2 = (12.984733724851393, -0.6352812071330611)
G_2 = (9.364733724851392, -0.48861454046639474)
I_2 = (13.560600351508915, -0.5686145404663945)
K_2 = (15.560441627729189, -0.23600883133958614)
L_2 = (15.5861499592764, -3.372425280099302)
M_2 = (20.676399605624137, -3.989425237232361)
N_2 = (20.727816268718556, -0.18459216824516456)
S_2 = Point(xAxis)
T_2 = Point(xAxis)
T1: "u_{n+1} =   u_{n} + " + r + ""
c = OrthogonalLine(D, xAxis)
p_3 = OrthogonalLine(F, xAxis)
q_3 = OrthogonalLine(H, xAxis)
r_3 = OrthogonalLine(J, xAxis)
s_3 = OrthogonalLine(L, xAxis)
t_3 = OrthogonalLine(O_2, xAxis)
a_4 = OrthogonalLine(Q, xAxis)
b_4 = OrthogonalLine(S, xAxis)
c_4 = OrthogonalLine(U, xAxis)
d_4 = OrthogonalLine(W, xAxis)
e_4 = OrthogonalLine(Z_2, xAxis)
f_4 = OrthogonalLine(B_1, xAxis)
g_4 = OrthogonalLine(D_1, xAxis)
h_4 = OrthogonalLine(F_1, xAxis)
i_4 = OrthogonalLine(H_1, xAxis)
j_4 = OrthogonalLine(J_1, xAxis)
O = Intersect(j_4, xAxis)
N_1 = Intersect(i_4, xAxis)
O_1 = Intersect(h_4, xAxis)
P_1 = Intersect(g_4, xAxis)
Q_1 = Intersect(f_4, xAxis)
R_1 = Intersect(e_4, xAxis)
S_1 = Intersect(d_4, xAxis)
T_1 = Intersect(c_4, xAxis)
U_1 = Intersect(b_4, xAxis)
V_1 = Intersect(a_4, xAxis)
W_1 = Intersect(t_3, xAxis)
Z_1 = Intersect(s_3, xAxis)
A_2 = Intersect(r_3, xAxis)
B_2 = Intersect(q_3, xAxis)
C_2 = Intersect(p_3, xAxis)
D_2 = Intersect(c, xAxis)
k_4 = Segment(D_2, D)
l_4 = Segment(F, C_2)
m_4 = Segment(H, B_2)
n_4 = Segment(A_2, J)
p_4 = Segment(L, Z_1)
q_4 = Segment(O_2, W_1)
r_4 = Segment(Q, V_1)
s_4 = Segment(S, U_1)
t_4 = Segment(T_1, T)
a_5 = Segment(S_1, V)
b_5 = Segment(R_1, Y)
c_5 = Segment(Q_1, A_1)
d_5 = Segment(P_1, C_1)
e_5 = Segment(O_1, E_1)
f_5 = Segment(N_1, G_1)
g_5 = Segment(O, I_1)
T8: " u_n=" + (LaTeX[x(u_0)]) + "+" + (LaTeX[r]) + "n"