Author: Daniel Mentrard

Taille

a³

b³

ab²

ab²

ab²

a²b

a²b

a²b

Desenganchar

(a + b) ³ = a³ + 3 a²b + 3ab² + b³

B_1 = (4.6000000000000005, 0)
Vistas = (4.202776206000955, 0.13609982695893888)
xa: x(Vistas)
sinphi: sin(xa)
cosphi: cos(xa)
ya: y(Vistas)
sintheta: sin(ya)
Zoom = 1 (slider from 0.2 to 1, step 0.1)
xy: -(Zoom) * cosphi * sintheta
g = 1 (slider from -5 to 5, step 0.1)
X: (x(B_1) + Zoom * sinphi, y(B_1) + xy)
u = Vector(B_1, X)
O = (7.390766389862363, 1.0749359192401589)
k = 1 (slider from -5 to 5, step 0.1)
costheta: cos(ya)
Z: (x(B_1) + 0.0, y(B_1) + Zoom * costheta)
w = Vector(B_1, Z)
a = OrthogonalLine(Vistas, yAxis)
b = OrthogonalLine(Vistas, xAxis)
c: cos(ya)
Y: (x(B_1) + Zoom * cosphi, y(B_1) + Zoom * sinphi * sintheta)
v = Vector(B_1, Y)
A_1 = Translate(O, Vector[g * u])
d = Segment(O, A_1)
B_2 = Translate(O, Vector[g * v])
e = Segment(O, B_2)
D_1 = Mirror(B_2, O)
E_1 = Mirror(A_1, O)
h = Segment(D_1, O)
i = Segment(E_1, O)
G_1 = Translate(A_1, v)
H_1 = Translate(D_1, u)
I = Mirror(G_1, B_2)
J = Mirror(H_1, D_1)
B = Translate(J, w)
A = Translate(I, w)
D = Translate(G_1, w)
C = Translate(H_1, w)
poly1', j', i', g', h' = Polygon(B, A, D, C)
H = Mirror(B, O)
G = Mirror(A, O)
F = Mirror(D, O)
E = Mirror(C, O)
poly1'', j'', i'', g'', h'' = Polygon(H, G, F, E)
poly2, j'_1, g''_1, i''_1, h'_1 = Polygon(B, F, G, C)
poly3, i'_1, h''_1, j''_1, g'_1 = Polygon(A, E, H, D)
L = Intersect(h', h'_1)
M = Intersect(h'', h''_1)
P = Intersect(h', h'_1)
R = Point(j''_1)
l = Line(R, h''_1)
m = Line(R, g')
S = Intersect(m, i''_1)
f = Segment(D, R)
j = Line(S, i'')
K = Intersect(j, j'_1)
N = Intersect(i'_1, l)
p = Circle(D, i' * f / j''_1)
Q, O_1 = Intersect(p, i')
n = Line(Q, j')
T = Intersect(h', h'_1)
U = Intersect(n, h')
q = Line(Q, j''_1)
r = Line(U, i''_1)
s = Segment(S, R)
t = Circle(R, s * f / j''_1)
V, P_1 = Intersect(t, s)
a1 = Line(V, j''_1)
W = Intersect(a1, g')
b1 = Line(W, i')
A1 = Intersect(n, b1)
B1 = Intersect(l, q)
c1 = Line(B1, s)
d1 = Line(V, l)
C1 = Intersect(d1, c1)
e1 = Segment(A1, C1)
D1 = Intersect(b1, j')
poly1, a1_1, w_1, v_1, c1_1 = Polygon(A1, W, V, C1)
poly4, a1_2, q_1, b1_1, c1_2 = Polygon(A1, Q, B1, C1)
poly5, r_1, b1_2, q_2, d_1 = Polygon(R, B1, Q, D)
f1 = Line(B1, n)
E1 = Intersect(j, r)
poly6, e1_1, c1_3, a1_3, u_1 = Polygon(E1, C1, A1, U)
poly7, e1_2, s_1, c_1, u_2 = Polygon(E1, S, C, U)
g1 = Segment(K, N)
h1 = Line(C1, i')
F1 = Intersect(h1, g1)
poly9, k_2, f1_1, c1_4, e1_4 = Polygon(K, F1, C1, E1)
poly12, q_3, a_1, n_1, b1_3 = Polygon(Q, A, N, B1)
i1 = Line(B1, j''_1)
G1 = Intersect(h'', h''_1)
H1 = Intersect(h'', h''_1)
I1 = Intersect(h'', h''_1)
J1 = Intersect(i1, h'')
j1 = Line(V, j''_1)
K1 = Intersect(j'', j1)
k1 = Line(J1, g'')
L1 = Intersect(i'', g''_1)
M1 = Intersect(i'', g''_1)
N1 = Intersect(k1, i'')
l1 = Line(C1, i1)
O1 = Intersect(k1, l1)
poly13, c1_6, v_2, k1_1, o1 = Polygon(C1, V, K1, O1)
m1 = Line(O1, h'')
P1 = Intersect(m1, g'')
poly14, n1, f_1, p1, o1_1 = Polygon(N1, F, P1, O1)
poly15, e1_5, n1_1, o1_2, c1_7 = Polygon(E1, N1, O1, C1)
poly16, k_4, e1_6, n1_2, f_2 = Polygon(K, E1, N1, F)
poly17, c1_8, f1_4, p1_1, o1_3 = Polygon(C1, F1, P1, O1)
poly18, f1_5, k_5, f_3, p1_2 = Polygon(F1, K, F, P1)
poly20, o1_5, j1_1, e_1, p1_4 = Polygon(O1, J1, E, P1)
poly21, c1_{10}, b1_4, j1_2, o1_6 = Polygon(C1, B1, J1, O1)
poly22, c1_{11}, b1_5, n_2, f1_7 = Polygon(C1, B1, N, F1)
poly23, b1_6, n_3, e_2, j1_3 = Polygon(B1, N, E, J1)
C_1 = Midpoint(E1, K1)
z = Vector(O, C_1)
o = 0 (slider from 0 to 1, step 0.1)
F_1 = Midpoint(B1, P1)
z_1 = Vector(O, F_1)
B1' = Translate(B1, Vector[o * z_1])
N' = Translate(N, Vector[o * z_1])
E' = Translate(E, Vector[o * z_1])
J1' = Translate(J1, Vector[o * z_1])
poly23', b1', n', e', j1' = Polygon(B1', N', E', J1')
C1' = Translate(C1, Vector[o * z_1])
B1'_1 = Translate(B1, Vector[o * z_1])
N'_1 = Translate(N, Vector[o * z_1])
F1' = Translate(F1, Vector[o * z_1])
poly22', c1', b1'_1, n'_1, f1' = Polygon(C1', B1'_1, N'_1, F1')
O1' = Translate(O1, Vector[o * z_1])
J1'_1 = Translate(J1, Vector[o * z_1])
E'_1 = Translate(E, Vector[o * z_1])
P1' = Translate(P1, Vector[o * z_1])
poly20', o1', j1'_1, e'_1, p1' = Polygon(O1', J1'_1, E'_1, P1')
C1'_1 = Translate(C1, Vector[o * z_1])
B1'_2 = Translate(B1, Vector[o * z_1])
J1'_2 = Translate(J1, Vector[o * z_1])
O1'_1 = Translate(O1, Vector[o * z_1])
poly21', c1'_1, b1'_2, j1'_2, o1'_1 = Polygon(C1'_1, B1'_2, J1'_2, O1'_1)
poly24, n'_2, f1'_1, p1'_1, e'_2 = Polygon(N'_1, F1', P1', E'_1)
poly25, f1'_2, c1'_2, o1'_2, p1'_2 = Polygon(F1', C1'_1, O1'_1, P1')
I_1 = Midpoint(D1, B1)
g_1 = Vector(O, I_1)
A1' = Translate(A1, Vector[o * g_1])
D1' = Translate(D1, Vector[o * g_1])
F1'_1 = Translate(F1, Vector[o * g_1])
C1'_2 = Translate(C1, Vector[o * g_1])
poly11', a1', d1', f1'_3, c1'_3 = Polygon(A1', D1', F1'_1, C1'_2)
Q' = Translate(Q, Vector[o * g_1])
A' = Translate(A, Vector[o * g_1])
N'_2 = Translate(N, Vector[o * g_1])
B1'_3 = Translate(B1, Vector[o * g_1])
poly12', q', a', n'_3, b1'_3 = Polygon(Q', A', N'_2, B1'_3)
J_1 = Midpoint(A1, R)
h_1 = Vector(O, J_1)
R' = Translate(R, Vector[o * h_1])
B1'_4 = Translate(B1, Vector[o * h_1])
Q'_1 = Translate(Q, Vector[o * h_1])
D' = Translate(D, Vector[o * h_1])
poly5', r', b1'_4, q'_1, d' = Polygon(R', B1'_4, Q'_1, D')
A1'_1 = Translate(A1, Vector[o * h_1])
W' = Translate(W, Vector[o * h_1])
V' = Translate(V, Vector[o * h_1])
C1'_3 = Translate(C1, Vector[o * h_1])
poly1'_1, a1'_1, w', v', c1'_4 = Polygon(A1'_1, W', V', C1'_3)
K_1 = Midpoint(C1, H)
i_1 = Vector(O, K_1)
poly26, o1_7, j1_4, h_2, k1_2 = Polygon(O1, J1, H, K1)
O1'_2 = Translate(O1, Vector[o * i_1])
J1'_3 = Translate(J1, Vector[o * i_1])
H' = Translate(H, Vector[o * i_1])
K1' = Translate(K1, Vector[o * i_1])
poly26', o1'_3, j1'_3, h'_2, k1' = Polygon(O1'_2, J1'_3, H', K1')
poly27, b1_7, c1_{12}, v_3, r_2 = Polygon(B1, C1, V, R)
B1'_5 = Translate(B1, Vector[o * i_1])
C1'_4 = Translate(C1, Vector[o * i_1])
V'_1 = Translate(V, Vector[o * i_1])
R'_1 = Translate(R, Vector[o * i_1])
poly27', b1'_5, c1'_5, v'_1, r'_1 = Polygon(B1'_5, C1'_4, V'_1, R'_1)
L_1 = Midpoint(F, F1)
j_1 = Vector(O, L_1)
E1' = Translate(E1, Vector[o * z])
N1' = Translate(N1, Vector[o * z])
O1'_3 = Translate(O1, Vector[o * z])
C1'_5 = Translate(C1, Vector[o * z])
poly15', e1', n1', o1'_4, c1'_6 = Polygon(E1', N1', O1'_3, C1'_5)
B' = Translate(B, Vector[o * z])
F' = Translate(F, Vector[o * z])
G' = Translate(G, Vector[o * z])
C' = Translate(C, Vector[o * z])
poly28, s_2, v_4, k1_3, g_2 = Polygon(S, V, K1, G)
S' = Translate(S, Vector[o * z])
V'_2 = Translate(V, Vector[o * z])
K1'_1 = Translate(K1, Vector[o * z])
G'_1 = Translate(G, Vector[o * z])
poly28', s', v'_2, k1'_1, g'_2 = Polygon(S', V'_2, K1'_1, G'_1)
M_1 = Midpoint(A1, S)
l_1 = Vector(O, M_1)
poly29, u_4, a1_5, c1_{13}, e1_7 = Polygon(U, A1, C1, E1)
U' = Translate(U, Vector[o * l_1])
A1'_2 = Translate(A1, Vector[o * l_1])
C1'_6 = Translate(C1, Vector[o * l_1])
E1'_1 = Translate(E1, Vector[o * l_1])
poly29', u', a1'_2, c1'_7, e1'_1 = Polygon(U', A1'_2, C1'_6, E1'_1)
poly30, c_2, w_2, v_5, s_3 = Polygon(C, W, V, S)
C'_1 = Translate(C, Vector[o * l_1])
W'_1 = Translate(W, Vector[o * l_1])
V'_3 = Translate(V, Vector[o * l_1])
S'_1 = Translate(S, Vector[o * l_1])
poly30', c'_1, w'_1, v'_3, s'_1 = Polygon(C'_1, W'_1, V'_3, S'_1)
N1'_1 = Translate(N1, Vector[o * j_1])
F'_1 = Translate(F, Vector[o * j_1])
P1'_1 = Translate(P1, Vector[o * j_1])
O1'_4 = Translate(O1, Vector[o * j_1])
poly14', n1'_1, f'_1, p1'_3, o1'_5 = Polygon(N1'_1, F'_1, P1'_1, O1'_4)
E1'_2 = Translate(E1, Vector[o * j_1])
N1'_2 = Translate(N1, Vector[o * j_1])
O1'_5 = Translate(O1, Vector[o * j_1])
C1'_7 = Translate(C1, Vector[o * j_1])
poly15'_1, e1'_2, n1'_2, o1'_6, c1'_8 = Polygon(E1'_2, N1'_2, O1'_5, C1'_7)
poly31, f1_8, k_6, f_4, p1_5 = Polygon(F1, K, F, P1)
F1'_2 = Translate(F1, Vector[o * j_1])
K' = Translate(K, Vector[o * j_1])
F'_2 = Translate(F, Vector[o * j_1])
P1'_2 = Translate(P1, Vector[o * j_1])
poly31', f1'_4, k', f'_2, p1'_4 = Polygon(F1'_2, K', F'_2, P1'_2)
N_1 = Midpoint(A1, K)
m_1 = Vector(O, N_1)
poly8, f1_2, k_1, e1_3, c1_5 = Polygon(F1, K, E1, C1)
F1'_3 = Translate(F1, Vector[o * m_1])
K'_1 = Translate(K, Vector[o * m_1])
F'_3 = Translate(F, Vector[o * m_1])
P1'_3 = Translate(P1, Vector[o * m_1])
F1'_4 = Translate(F1, Vector[o * m_1])
K'_2 = Translate(K, Vector[o * m_1])
E1'_3 = Translate(E1, Vector[o * m_1])
C1'_8 = Translate(C1, Vector[o * m_1])
poly8', f1'_5, k'_2, e1'_3, c1'_9 = Polygon(F1'_4, K'_2, E1'_3, C1'_8)
poly10, a_2, b_1, u_3, q_4 = Polygon(A, B, U, Q)
Q'_2 = Translate(Q, Vector[o * m_1])
poly11, f1'_6, c1'_{10}, e1'_4, k'_1 = Polygon(F1'_2, C1'_7, E1'_2, K')
poly19, k'_3, e1'_5, n1'_3, f'_3 = Polygon(K', E1'_2, N1'_2, F'_2)
poly32, c1'_{11}, f1'_7, p1'_5, o1'_7 = Polygon(C1'_7, F1'_2, P1'_2, O1'_5)
poly33, c1'_{12}, v'_4, k1'_2, o1'_8 = Polygon(C1'_5, V'_2, K1'_1, O1'_3)
poly34, o1'_9, n1'_4, g'_3, k1'_3 = Polygon(O1'_3, N1', G'_1, K1'_1)
poly35, c1'_{13}, e1'_6, s'_2, v'_5 = Polygon(C1'_5, E1', S', V'_2)
poly36, e1'_7, n1'_5, g'_4, s'_3 = Polygon(E1', N1', G'_1, S')
poly37, b1'_6, c1'_{14}, v'_6, r'_2 = Polygon(B1'_4, C1'_3, V', R')
poly38, q'_3, a1'_3, c1'_{15}, b1'_7 = Polygon(Q'_1, A1'_1, C1'_3, B1'_4)
poly39, d'_1, w'_2, v'_7, r'_3 = Polygon(D', W', V', R')
poly40, q'_4, d'_2, w'_3, a1'_4 = Polygon(Q'_1, D', W', A1'_1)
poly41, u'_2, c'_2, s'_4, e1'_8 = Polygon(U', C'_1, S'_1, E1'_1)
poly42, c1'_{16}, v'_8, s'_5, e1'_9 = Polygon(C1'_6, V'_3, S'_1, E1'_1)
poly43, a1'_5, w'_4, v'_9, c1'_{17} = Polygon(A1'_2, W'_1, V'_3, C1'_6)
poly44, a1'_6, u'_3, c'_3, w'_5 = Polygon(A1'_2, U', C'_1, W'_1)
poly45, b1'_8, j1'_4, h'_3, r'_4 = Polygon(B1'_5, J1'_3, H', R'_1)
poly46, b1'_9, c1'_{18}, o1'_{10}, j1'_5 = Polygon(B1'_5, C1'_4, O1'_2, J1'_3)
poly47, r'_5, v'_{10}, k1'_4, h'_4 = Polygon(R'_1, V'_1, K1', H')
poly48, c1'_{19}, v'_{11}, k1'_5, o1'_{11} = Polygon(C1'_4, V'_1, K1', O1'_2)
p_1 = Vector(K, B)
Q_1 = Translate(F1'_4, p_1)
R_1 = Translate(K'_2, p_1)
S_1 = Translate(E1'_3, p_1)
T_1 = Translate(C1'_8, p_1)
poly8'', q_5, r_3, s_4, t_1 = Polygon(Q_1, R_1, S_1, T_1)
poly49, q_6, f1'_8, c1'_{20}, t_2 = Polygon(Q_1, F1'_4, C1'_8, T_1)
poly50, q_7, r_4, k'_4, f1'_9 = Polygon(Q_1, R_1, K'_2, F1'_4)
poly51, r_5, s_5, e1'_{10}, k'_5 = Polygon(R_1, S_1, E1'_3, K'_2)
poly52, s_6, t_3, c1'_{21}, e1'_{11} = Polygon(S_1, T_1, C1'_8, E1'_3)
poly53, n'_4, f1'_{10}, c1'_{22}, b1'_{10} = Polygon(N'_2, F1'_1, C1'_2, B1'_3)
poly54, a'_1, d1'_1, f1'_{11}, n'_5 = Polygon(A', D1', F1'_1, N'_2)
poly55, q'_2, a1'_7, c1'_{23}, b1'_{11} = Polygon(Q', A1', C1'_2, B1'_3)
poly56, a'_2, d1'_2, a1'_8, q'_5 = Polygon(A', D1', A1', Q')
b_2 = Segment(A, B)
d_2 = Segment(B, F)
i_2 = Segment(B, C)
j_2 = Segment(C, G)
l_2 = Segment(C, D)
U_1 = Midpoint(A1'_1, R')
V_1 = Midpoint(E1'_2, P1'_2)
W_1 = Midpoint(C1'_1, E'_1)
Z_1 = Midpoint(S_1, F1'_4)
A_2 = Midpoint(E1', K1'_1)
C_2 = Midpoint(C'_1, C1'_6)
D_2 = Midpoint(A1', N'_2)
E_2 = Midpoint(V'_1, J1'_3)