Animation

Même périmètre mais pas même aire

A = Intersect(xAxis, yAxis)
B = Point(yAxis)
C = Point(xAxis)
c_2 = CircleArc(A, B, C)
A'_1 = Mirror(A, xAxis)
B'_1 = Mirror(B, xAxis)
C'_1 = Mirror(C, xAxis)
c'_1 = Arc(Mirror[Circle[A, B], xAxis], B'_1, C'_1)
u = Vector(C, B)
B''_1 = Translate(B'_1, u)
C''_1 = Translate(C'_1, u)
c''_1 = Arc(Translate[Mirror[Circle[A, B], xAxis], u], B''_1, C''_1)
v = Vector(C, B'_1)
A'_2 = Translate(A, v)
B'_2 = Translate(B, v)
C'_2 = Translate(C, v)
c'_2 = Arc(Translate[Circle[A, B], v], B'_2, C'_2)
E = Point(xAxis)
w = Vector(C, E)
A'_3 = Translate(A, w)
B'_3 = Translate(B, w)
C'_3 = Translate(C, w)
c'_3 = Arc(Translate[Circle[A, B], w], B'_3, C'_3)
z = Vector(A'_1, B'_2)
a = Vector(A'_1, A'_3)
B'''_1 = Translate(B''_1, a)
C'''_1 = Translate(C''_1, a)
c'''_1 = Arc(Translate[Translate[Mirror[Circle[A, B], xAxis], u], a], B'''_1, C'''_1)
D = Translate(B'_2, a)
F = Translate(C'_2, a)
d = Arc(Translate[Translate[Circle[A, B], v], a], D, F)
G = Mirror(B'_2, yAxis)
H = Mirror(C'_2, yAxis)
e = Arc(Mirror[Translate[Circle[A, B], v], yAxis], G, H)
G'_1 = Translate(G, a)
H'_1 = Translate(H, a)
e'_1 = Arc(Translate[Mirror[Translate[Circle[A, B], v], yAxis], a], G'_1, H'_1)
B'''_2 = Mirror(B''_1, yAxis)
C'''_2 = Mirror(C''_1, yAxis)
c = Arc(Mirror[Translate[Mirror[Circle[A, B], xAxis], u], yAxis], B'''_2, C'''_2)
I = Point(xAxis)
b = Vector(A'_1, I)
A' = Translate(A, b)
B' = Translate(B, b)
C' = Translate(C, b)
c'_4 = Arc(Translate[Circle[A, B], b], B', C')
J = Translate(B'_1, b)
K = Translate(C'_1, b)
f = Arc(Translate[Mirror[Circle[A, B], xAxis], b], J, K)
L = Translate(B'_2, b)
M = Translate(C'_2, b)
g = Arc(Translate[Translate[Circle[A, B], v], b], L, M)
B'''_3 = Translate(B''_1, b)
C'''_3 = Translate(C''_1, b)
c'''_3 = Arc(Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], B'''_3, C'''_3)
N = (-3, -1)
O = Point(yAxis)
h = Vector(N, O)
P = (3, -1)
i = Vector(P, O)
G'_2 = Translate(G, h)
H'_2 = Translate(H, h)
e'_2 = Arc(Translate[Mirror[Translate[Circle[A, B], v], yAxis], h], G'_2, H'_2)
Q = Translate(B'_2, i)
R = Translate(C'_2, i)
k = Arc(Translate[Translate[Circle[A, B], v], i], Q, R)
S = Point(yAxis)
j = Vector(N, S)
l = Vector(P, S)
T = Translate(B'''_2, j)
U = Translate(C'''_2, j)
p = Arc(Translate[Mirror[Translate[Mirror[Circle[A, B], xAxis], u], yAxis], j], T, U)
B''' = Translate(B''_1, l)
C''' = Translate(C''_1, l)
c''' = Arc(Translate[Translate[Mirror[Circle[A, B], xAxis], u], l], B''', C''')
V = (5, -1)
W = (5, -8)
m = Vector(V, W)
Z = Translate(B'''_1, l)
A_1 = Translate(C'''_1, l)
q = Arc(Translate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], a], l], Z, A_1)
B_1 = Translate(B'_3, m)
C_1 = Translate(C'_3, m)
r = Arc(Translate[Translate[Circle[A, B], w], m], B_1, C_1)
D_1 = Translate(G'_1, h)
E_1 = Translate(H'_1, h)
s = Arc(Translate[Translate[Mirror[Translate[Circle[A, B], v], yAxis], a], h], D_1, E_1)
F_1 = (4, -1)
G_1 = (4, -5)
n = Vector(F_1, G_1)
B''_2 = Translate(B', a)
C''_2 = Translate(C', a)
c''_2 = Arc(Translate[Translate[Circle[A, B], b], a], B''_2, C''_2)
J'_1 = Translate(J, a)
K'_1 = Translate(K, a)
f'_1 = Arc(Translate[Translate[Mirror[Circle[A, B], xAxis], b], a], J'_1, K'_1)
L'_1 = Translate(L, a)
M'_1 = Translate(M, a)
g'_1 = Arc(Translate[Translate[Translate[Circle[A, B], v], b], a], L'_1, M'_1)
H_1 = Translate(B'''_3, a)
I_1 = Translate(C'''_3, a)
t_1 = Arc(Translate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], a], H_1, I_1)
J_1 = Intersect(c''_2, t_1, 1)
K_1 = Intersect(g'_1, t_1, 1)
a_1 = Segment(J_1, K_1)
L_1 = Mirror(H_1, a_1)
M_1 = Mirror(I_1, a_1)
t' = Arc(Mirror[Translate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], a], a_1], L_1, M_1)
N_1 = (11, -3)
D'_1 = Rotate(D, 180*°, N_1)
F'_1 = Rotate(F, 180*°, N_1)
d'_1 = Arc(Rotate[Translate[Translate[Circle[A, B], v], a], 180*°, N_1], D'_1, F'_1)
D'' = Translate(D'_1, i)
F'' = Translate(F'_1, i)
d'' = Arc(Translate[Rotate[Translate[Translate[Circle[A, B], v], a], 180*°, N_1], i], D'', F'')
B''_3 = Translate(B', m)
C''_3 = Translate(C', m)
c'' = Arc(Translate[Translate[Circle[A, B], b], m], B''_3, C''_3)
J'_2 = Translate(J, m)
K'_2 = Translate(K, m)
f'_2 = Arc(Translate[Translate[Mirror[Circle[A, B], xAxis], b], m], J'_2, K'_2)
O_1 = (19, 3)
P_1 = (19, -3)
Q_1 = (27, -3)
L'_2 = Rotate(L, 180*°, P_1)
M'_2 = Rotate(M, 180*°, P_1)
g'_2 = Arc(Rotate[Translate[Translate[Circle[A, B], v], b], 180*°, P_1], L'_2, M'_2)
R_1 = Rotate(B'''_3, 180*°, O_1)
S_1 = Rotate(C'''_3, 180*°, O_1)
c_1 = Arc(Rotate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], 180*°, O_1], R_1, S_1)
T_1 = Rotate(L'_1, 180*°, Q_1)
U_1 = Rotate(M'_1, 180*°, Q_1)
t_3 = Arc(Rotate[Translate[Translate[Translate[Circle[A, B], v], b], a], 180*°, Q_1], T_1, U_1)
V_1 = (16, -7)
u_1 = Vector(O_1, V_1)
W_1 = Translate(R_1, u_1)
Z_1 = Translate(S_1, u_1)
e_1 = Arc(Translate[Rotate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], 180*°, O_1], u_1], W_1, Z_1)
L'' = Translate(L'_2, i)
M'' = Translate(M'_2, i)
g'' = Arc(Translate[Rotate[Translate[Translate[Circle[A, B], v], b], 180*°, P_1], i], L'', M'')
A_2 = Translate(B''_2, m)
B_2 = Translate(C''_2, m)
f_1 = Arc(Translate[Translate[Translate[Circle[A, B], b], a], m], A_2, B_2)
C_2 = Translate(J'_1, m)
D_2 = Translate(K'_1, m)
g_1 = Arc(Translate[Translate[Translate[Mirror[Circle[A, B], xAxis], b], a], m], C_2, D_2)
E_2 = Translate(L_1, m)
F_2 = Translate(M_1, m)
t''_1 = Arc(Translate[Mirror[Translate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], a], a_1], m], E_2, F_2)
G_2 = Translate(T_1, i)
H_2 = Translate(U_1, i)
h_1 = Arc(Translate[Rotate[Translate[Translate[Translate[Circle[A, B], v], b], a], 180*°, Q_1], i], G_2, H_2)
t = -10 (slider from -10 to 50, step 0.1)
D'_2 = Rotate(D, 180*°, N_1)
F'_2 = Rotate(F, 180*°, N_1)
D' = Rotate(D, 3.141592653589793 * t / 20, N_1)
F' = Rotate(F, 3.141592653589793 * t / 20, N_1)
d' = Arc(Rotate[Translate[Translate[Circle[A, B], v], a], 3.141592653589793 * t / 20, N_1], D', F')
I_2 = Rotate(B'''_3, 3.141592653589793 * t / 20, O_1)
J_2 = Rotate(C'''_3, 3.141592653589793 * t / 20, O_1)
k_1 = Arc(Rotate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], 3.141592653589793 * t / 20, O_1], I_2, J_2)
L' = Rotate(L, 3.141592653589793 * t / 20, P_1)
M' = Rotate(M, 3.141592653589793 * t / 20, P_1)
g' = Arc(Rotate[Translate[Translate[Circle[A, B], v], b], 3.141592653589793 * t / 20, P_1], L', M')
K_2 = Rotate(L'_1, 3.141592653589793 * t / 20, Q_1)
L_2 = Rotate(M'_1, 3.141592653589793 * t / 20, Q_1)
p_1 = Arc(Rotate[Translate[Translate[Translate[Circle[A, B], v], b], a], 3.141592653589793 * t / 20, Q_1], K_2, L_2)
G' = Translate(G, Vector[h * (t - 20) / 20])
H' = Translate(H, Vector[h * (t - 20) / 20])
e' = Arc(Translate[Mirror[Translate[Circle[A, B], v], yAxis], Vector[h * (t - 20) / 20]], G', H')
M_2 = Translate(B'''_2, Vector[j * (t - 20) / 20])
N_2 = Translate(C'''_2, Vector[j * (t - 20) / 20])
c' = Arc(Translate[Mirror[Translate[Mirror[Circle[A, B], xAxis], u], yAxis], Vector[j * (t - 20) / 20]], M_2, N_2)
O_2 = Translate(B''_1, Vector[l * (t - 20) / 20])
P_2 = Translate(C''_1, Vector[l * (t - 20) / 20])
q_1 = Arc(Translate[Translate[Mirror[Circle[A, B], xAxis], u], Vector[l * (t - 20) / 20]], O_2, P_2)
Q_2 = Translate(B'_2, Vector[i * (t - 20) / 20])
R_2 = Translate(C'_2, Vector[i * (t - 20) / 20])
r_1 = Arc(Translate[Translate[Circle[A, B], v], Vector[i * (t - 20) / 20]], Q_2, R_2)
S_2 = Translate(D'_1, Vector[i * (t - 20) / 20])
T_2 = Translate(F'_1, Vector[i * (t - 20) / 20])
d_1 = Arc(Translate[Rotate[Translate[Translate[Circle[A, B], v], a], 180*°, N_1], Vector[i * (t - 20) / 20]], S_2, T_2)
U_2 = Translate(B'''_1, Vector[l * (t - 20) / 20])
V_2 = Translate(C'''_1, Vector[l * (t - 20) / 20])
s_1 = Arc(Translate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], a], Vector[l * (t - 20) / 20]], U_2, V_2)
W_2 = Translate(B'_3, Vector[m * (t - 20) / 20])
Z_2 = Translate(C'_3, Vector[m * (t - 20) / 20])
d_2 = Arc(Translate[Translate[Circle[A, B], w], Vector[m * (t - 20) / 20]], W_2, Z_2)
A_3 = Translate(G'_1, Vector[h * (t - 20) / 20])
B_3 = Translate(H'_1, Vector[h * (t - 20) / 20])
e_2 = Arc(Translate[Translate[Mirror[Translate[Circle[A, B], v], yAxis], a], Vector[h * (t - 20) / 20]], A_3, B_3)
B'' = Translate(B', Vector[m * (t - 20) / 20])
C'' = Translate(C', Vector[m * (t - 20) / 20])
f_2 = Arc(Translate[Translate[Circle[A, B], b], Vector[m * (t - 20) / 20]], B'', C'')
C_3 = Translate(B''_2, Vector[m * (t - 20) / 20])
D_3 = Translate(C''_2, Vector[m * (t - 20) / 20])
g_2 = Arc(Translate[Translate[Translate[Circle[A, B], b], a], Vector[m * (t - 20) / 20]], C_3, D_3)
J' = Translate(J, Vector[m * (t - 20) / 20])
K' = Translate(K, Vector[m * (t - 20) / 20])
f' = Arc(Translate[Translate[Mirror[Circle[A, B], xAxis], b], Vector[m * (t - 20) / 20]], J', K')
E_3 = Translate(J'_1, Vector[m * (t - 20) / 20])
F_3 = Translate(K'_1, Vector[m * (t - 20) / 20])
h_2 = Arc(Translate[Translate[Translate[Mirror[Circle[A, B], xAxis], b], a], Vector[m * (t - 20) / 20]], E_3, F_3)
G_3 = Translate(L_1, Vector[m * (t - 20) / 20])
H_3 = Translate(M_1, Vector[m * (t - 20) / 20])
t'' = Arc(Translate[Mirror[Translate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], a], a_1], Vector[m * (t - 20) / 20]], G_3, H_3)
I_3 = Translate(I_2, Vector[u_1 * (t - 20) / 20])
J_3 = Translate(J_2, Vector[u_1 * (t - 20) / 20])
K_3 = Rotate(L'_1, 3.141592653589793, Q_1)
L_3 = Rotate(M'_1, 3.141592653589793, Q_1)
k_2 = Arc(Rotate[Translate[Translate[Translate[Circle[A, B], v], b], a], 3.141592653589793, Q_1], K_3, L_3)
M_3 = Rotate(B'''_3, 3.141592653589793, O_1)
N_3 = Rotate(C'''_3, 3.141592653589793, O_1)
p_2 = Arc(Rotate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], 3.141592653589793, O_1], M_3, N_3)
O_3 = Translate(M_3, Vector[u_1 * (t - 20) / 20])
P_3 = Translate(N_3, Vector[u_1 * (t - 20) / 20])
q_2 = Arc(Translate[Rotate[Translate[Translate[Mirror[Circle[A, B], xAxis], u], b], 3.141592653589793, O_1], Vector[u_1 * (t - 20) / 20]], O_3, P_3)
Q_3 = Translate(L'_2, Vector[i * (t - 20) / 20])
R_3 = Translate(M'_2, Vector[i * (t - 20) / 20])
r_2 = Arc(Translate[Rotate[Translate[Translate[Circle[A, B], v], b], 180*°, P_1], Vector[i * (t - 20) / 20]], Q_3, R_3)
S_3 = Translate(K_3, Vector[i * (t - 20) / 20])
T_3 = Translate(L_3, Vector[i * (t - 20) / 20])
s_2 = Arc(Translate[Rotate[Translate[Translate[Translate[Circle[A, B], v], b], a], 3.141592653589793, Q_1], Vector[i * (t - 20) / 20]], S_3, T_3)