Interprétations de la fraction 4/3

C'est la taille de l'un des morceaux obtenus lorsqu'on partage un ensemble
de 4 unités en 3 parties.

une unité

une unité

une unité

une unité

4 unités à partager en 3

4/3

4/3

4/3

1° interprétation : 

2° interprétation :

une unité
partagée en 3

1/3

1/3

1/3

1/3

4/3

C'est 4 fois la taille du morceau obtenu en découpant chaque unité en 3.

Animation

une unité
partagée en 3

A = Intersect(xAxis, yAxis)
B = Point(yAxis)
C = Point(xAxis)
u = Vector(B, A)
v = Vector(A, C)
B'_1 = Translate(B, v)
poly1, a, c, b', b = Polygon(A, C, B'_1, B)
A'_1 = Translate(A, Vector[1.25 * v])
C'_1 = Translate(C, Vector[1.25 * v])
B''_1 = Translate(B'_1, Vector[1.25 * v])
B'_2 = Translate(B, Vector[1.25 * v])
poly1'_1, a', c', b'', b'_1 = Polygon(A'_1, C'_1, B''_1, B'_2)
A'_2 = Translate(A, Vector[2.5 * v])
C'_2 = Translate(C, Vector[2.5 * v])
D = Translate(B'_1, Vector[2.5 * v])
B'_3 = Translate(B, Vector[2.5 * v])
poly1'_2, a'_1, c'_1, d, b'_2 = Polygon(A'_2, C'_2, D, B'_3)
A'_3 = Translate(A, Vector[3.75 * v])
C'_3 = Translate(C, Vector[3.75 * v])
E = Translate(B'_1, Vector[3.75 * v])
B'_4 = Translate(B, Vector[3.75 * v])
poly1'_3, a'_2, c'_2, e, b'_3 = Polygon(A'_3, C'_3, E, B'_4)
I = (1, -2)
g = Vector(A, I)
A'_4 = Translate(A, g)
C'_4 = Translate(C, g)
J = Translate(B'_1, g)
B'_5 = Translate(B, g)
poly1'_4, a'_3, c'_3, j, b'_4 = Polygon(A'_4, C'_4, J, B'_5)
w = Vector(A'_1, C'_4)
F = (7, -2)
z = Vector(A'_2, F)
G = (10, -2)
f = Vector(A'_3, G)
H = Translate(A'_1, w)
K = Translate(C'_1, w)
B'''_1 = Translate(B''_1, w)
L = Translate(B'_2, w)
poly2, h, k, b''', l = Polygon(H, K, B'''_1, L)
M = Translate(A'_2, z)
N = Translate(C'_2, z)
D'_1 = Translate(D, z)
O = Translate(B'_3, z)
poly3, m, n, d', o = Polygon(M, N, D'_1, O)
P = Translate(A'_3, f)
Q = Translate(C'_3, f)
E'_1 = Translate(E, f)
R = Translate(B'_4, f)
poly4, p, q, e', r = Polygon(P, Q, E'_1, R)
poly5, i, q_1, e'_1, b'_5 = Polygon(I, Q, E'_1, B'_5)
poly6, a'_4, s, t, b'_6 = Polygon(A'_4, Translate[A'_4, Vector[4 / 3 * v]], Translate[B'_5, Vector[4 / 3 * v]], B'_5)
poly7, a_1, b_1, c_1, d_1 = Polygon(Translate[A'_4, Vector[4 / 3 * v]], Translate[A'_4, Vector[8 / 3 * v]], Translate[B'_5, Vector[8 / 3 * v]], Translate[B'_5, Vector[4 / 3 * v]])
poly8, e_1, f_1, g_1, h_1 = Polygon(Translate[A'_4, Vector[8 / 3 * v]], Translate[A'_4, Vector[12 / 3 * v]], Translate[B'_5, Vector[12 / 3 * v]], Translate[B'_5, Vector[8 / 3 * v]])
S = Point(yAxis)
u_1 = Vector(I, S)
T = (5, -2)
U = (5, -4)
v_1 = Vector(T, U)
V = (9, -2)
W = (10, -4)
w_1 = Vector(V, W)
A''_1 = Translate(A'_4, u_1)
Z = Translate(Translate[A'_4, Vector[4 / 3 * v]], u_1)
A_1 = Translate(Translate[B'_5, Vector[4 / 3 * v]], u_1)
B''_2 = Translate(B'_5, u_1)
poly6'_1, a'', z_1, a_2, b''_1 = Polygon(A''_1, Z, A_1, B''_2)
B_1 = Translate(Translate[A'_4, Vector[4 / 3 * v]], v_1)
C_1 = Translate(Translate[A'_4, Vector[8 / 3 * v]], v_1)
D_1 = Translate(Translate[B'_5, Vector[8 / 3 * v]], v_1)
E_1 = Translate(Translate[B'_5, Vector[4 / 3 * v]], v_1)
poly7'_1, b_2, c_2, d_2, e_2 = Polygon(B_1, C_1, D_1, E_1)
F_1 = Translate(Translate[A'_4, Vector[8 / 3 * v]], w_1)
G_1 = Translate(Translate[A'_4, Vector[12 / 3 * v]], w_1)
H_1 = Translate(Translate[B'_5, Vector[12 / 3 * v]], w_1)
I_1 = Translate(Translate[B'_5, Vector[8 / 3 * v]], w_1)
poly8'_1, f_2, g_2, h_2, i_1 = Polygon(F_1, G_1, H_1, I_1)
time = -10 (slider from -10 to 300, step 0.1)
A'_5 = Translate(A, Vector[(time - 50) / 10 * g])
C'_5 = Translate(C, Vector[(time - 50) / 10 * g])
J_1 = Translate(B'_1, Vector[(time - 50) / 10 * g])
B'_6 = Translate(B, Vector[(time - 50) / 10 * g])
poly1'_5, a'_5, c'_4, j_1, b'_7 = Polygon(A'_5, C'_5, J_1, B'_6)
K_1 = Translate(A'_1, Vector[(time - 50) / 10 * w])
L_1 = Translate(C'_1, Vector[(time - 50) / 10 * w])
M_1 = Translate(B''_1, Vector[(time - 50) / 10 * w])
N_1 = Translate(B'_2, Vector[(time - 50) / 10 * w])
poly9, k_1, l_1, m_1, n_1 = Polygon(K_1, L_1, M_1, N_1)
O_1 = Translate(A'_2, Vector[(time - 50) / 10 * z])
P_1 = Translate(C'_2, Vector[(time - 50) / 10 * z])
D' = Translate(D, Vector[(time - 50) / 10 * z])
Q_1 = Translate(B'_3, Vector[(time - 50) / 10 * z])
poly10, o_1, p_1, d'_1, q_2 = Polygon(O_1, P_1, D', Q_1)
R_1 = Translate(A'_3, Vector[(time - 50) / 10 * f])
S_1 = Translate(C'_3, Vector[(time - 50) / 10 * f])
E' = Translate(E, Vector[(time - 50) / 10 * f])
T_1 = Translate(B'_4, Vector[(time - 50) / 10 * f])
poly11, r_1, s_1, e'_2, t_1 = Polygon(R_1, S_1, E', T_1)
U_1 = Translate(A'_4, Vector[(time - 80) / 10 * u_1])
V_1 = Translate(Translate[A'_4, Vector[4 / 3 * v]], Vector[(time - 80) / 10 * u_1])
W_1 = Translate(Translate[B'_5, Vector[4 / 3 * v]], Vector[(time - 80) / 10 * u_1])
Z_1 = Translate(B'_5, Vector[(time - 80) / 10 * u_1])
poly6', u_2, v_2, w_2, z_2 = Polygon(U_1, V_1, W_1, Z_1)
A_2 = Translate(Translate[A'_4, Vector[4 / 3 * v]], Vector[(time - 80) / 10 * v_1])
B_2 = Translate(Translate[A'_4, Vector[8 / 3 * v]], Vector[(time - 80) / 10 * v_1])
C_2 = Translate(Translate[B'_5, Vector[8 / 3 * v]], Vector[(time - 80) / 10 * v_1])
D_2 = Translate(Translate[B'_5, Vector[4 / 3 * v]], Vector[(time - 80) / 10 * v_1])
poly7', a_3, b_3, c_3, d_3 = Polygon(A_2, B_2, C_2, D_2)
E_2 = Translate(Translate[A'_4, Vector[8 / 3 * v]], Vector[(time - 80) / 10 * w_1])
F_2 = Translate(Translate[A'_4, Vector[12 / 3 * v]], Vector[(time - 80) / 10 * w_1])
G_2 = Translate(Translate[B'_5, Vector[12 / 3 * v]], Vector[(time - 80) / 10 * w_1])
H_2 = Translate(Translate[B'_5, Vector[8 / 3 * v]], Vector[(time - 80) / 10 * w_1])
poly8', e_3, f_3, g_3, h_3 = Polygon(E_2, F_2, G_2, H_2)
I_2 = Intersect(b, a)
J_2 = (0, -8)
i_2 = Vector(I_2, J_2)
A' = Translate(A, i_2)
C' = Translate(C, i_2)
K_2 = Translate(B'_1, i_2)
B' = Translate(B, i_2)
poly1', a'_6, c'_5, k_2, b'_8 = Polygon(A', C', K_2, B')
A''_2 = Translate(A', Vector[1 / 3 * v])
A''_3 = Translate(A', Vector[2 / 3 * v])
B''_3 = Translate(B', Vector[2 / 3 * v])
B''_4 = Translate(B', Vector[1 / 3 * v])
poly12, j_2, a''_2, b''_2, b'_9 = Polygon(J_2, A''_2, B''_4, B')
poly13, b''_3, a''_1, a''_3, b''_4 = Polygon(B''_4, A''_2, A''_3, B''_3)
poly14, b''_5, a''_4, c'_6, k_3 = Polygon(B''_3, A''_3, C', K_2)
L_2 = (0, -10)
l_2 = Vector(J_2, L_2)
M_2 = (1, -10)
m_2 = Vector(A''_2, M_2)
N_2 = (2, -10)
n_2 = Vector(A''_3, N_2)
O_2 = Translate(J_2, l_2)
P_2 = Translate(A''_2, l_2)
B''' = Translate(B''_4, l_2)
B''_5 = Translate(B', l_2)
poly12'_1, o_2, p_2, b'''_1, b''_6 = Polygon(O_2, P_2, B''', B''_5)
Q_2 = Translate(B''_4, m_2)
R_2 = Translate(A''_2, m_2)
A'''_1 = Translate(A''_3, m_2)
S_2 = Translate(B''_3, m_2)
poly13'_1, q_3, r_2, a''', s_2 = Polygon(Q_2, R_2, A'''_1, S_2)
T_2 = Translate(B''_3, n_2)
A'''_2 = Translate(A''_3, n_2)
C''_1 = Translate(C', n_2)
U_2 = Translate(K_2, n_2)
poly14'_1, t_2, a'''_1, c'', u_3 = Polygon(T_2, A'''_2, C''_1, U_2)
A''_4 = Translate(A', Vector[1.25 * v])
C''_2 = Translate(C', Vector[1.25 * v])
V_2 = Translate(K_2, Vector[1.25 * v])
B''_6 = Translate(B', Vector[1.25 * v])
poly1'', a''_5, c''_1, v_3, b''_7 = Polygon(A''_4, C''_2, V_2, B''_6)
A''_5 = Translate(A', Vector[1.25 * v + 1 / 3 * v])
B''_7 = Translate(B', Vector[1.25 * v + 1 / 3 * v])
B''_8 = Translate(B', Vector[1.25 * v + 2 / 3 * v])
A''_6 = Translate(A', Vector[1.25 * v + 2 / 3 * v])
A'' = Translate(A', Vector[1.25 * v])
poly15, b''_8, b''_9, a''_6, a''_7 = Polygon(B''_6, B''_7, A''_5, A'')
poly16, b''_{10}, a''_8, a''_9, b''_{11} = Polygon(B''_7, A''_5, A''_6, B''_8)
W_2 = Intersect(c''_1, a''_5)
Z_2 = Intersect(v_3, c''_1)
poly17, b''_{12}, a''_{10}, w_3, z_3 = Polygon(B''_8, A''_6, W_2, Z_2)
A_3 = Intersect(c'', a'''_1)
i_3 = Vector(A'', A_3)
B_3 = Translate(B''_6, i_3)
C_3 = Translate(B''_7, i_3)
D_3 = Translate(A''_5, i_3)
A'''_3 = Translate(A'', i_3)
poly15'_1, b_4, c_4, d_4, a'''_2 = Polygon(B_3, C_3, D_3, A'''_3)
poly18, l_3, b''_{13}, c_5, d_5 = Polygon(L_2, B''_5, C_3, D_3)
E_3 = Translate(J_2, Vector[(time - 180) / 10 * l_2])
F_3 = Translate(A''_2, Vector[(time - 180) / 10 * l_2])
G_3 = Translate(B''_4, Vector[(time - 180) / 10 * l_2])
B'' = Translate(B', Vector[(time - 180) / 10 * l_2])
poly12', e_4, f_4, g_4, b''_{14} = Polygon(E_3, F_3, G_3, B'')
H_3 = Translate(B''_4, Vector[(time - 180) / 10 * m_2])
I_3 = Translate(A''_2, Vector[(time - 180) / 10 * m_2])
J_3 = Translate(A''_3, Vector[(time - 180) / 10 * m_2])
K_3 = Translate(B''_3, Vector[(time - 180) / 10 * m_2])
L_3 = Translate(B''_4, Vector[(time - 190) / 10 * m_2])
M_3 = Translate(A''_2, Vector[(time - 190) / 10 * m_2])
N_3 = Translate(A''_3, Vector[(time - 190) / 10 * m_2])
O_3 = Translate(B''_3, Vector[(time - 190) / 10 * m_2])
poly13', l_4, m_3, n_3, o_3 = Polygon(L_3, M_3, N_3, O_3)
P_3 = Translate(B''_3, Vector[(time - 200) / 10 * n_2])
Q_3 = Translate(A''_3, Vector[(time - 200) / 10 * n_2])
C'' = Translate(C', Vector[(time - 200) / 10 * n_2])
R_3 = Translate(K_2, Vector[(time - 200) / 10 * n_2])
poly14', p_3, q_4, c''_2, r_3 = Polygon(P_3, Q_3, C'', R_3)
S_3 = Translate(B''_6, Vector[(time - 220) / 10 * i_3])
T_3 = Translate(B''_7, Vector[(time - 220) / 10 * i_3])
U_3 = Translate(A''_5, Vector[(time - 220) / 10 * i_3])
A''' = Translate(A'', Vector[(time - 220) / 10 * i_3])
poly15', s_3, t_3, u_4, a'''_3 = Polygon(S_3, T_3, U_3, A''')