a²-b²
Author: Daniel Mentrard

a²

b²

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(a-b)

(a-b)

(a-b)

Área_{verde} = a²- b²

Área_{ \;  Trapecio}= \frac{ (2a + 2b) x (a - b) }{2 } = \frac{2 (a + b) x (a - b) }{2 } =(a + b) x (a - b)

Dos maneras de hacer la estimación de una superfície.

o = 9.3 (slider from -5 to 10, step 0.1)
Animación = 0 (slider from 0 to 13, step 0.01)
A = (-0.8100065146579789, -0.1750358306188944)
Zoom = 3.8 (slider from 1 to 5, step 0.1)
c = Circle(A, Zoom)
B = Point(c)
B' = Rotate(B, 90.0*°, A)
B'' = Rotate(B', 90.0*°, A)
B''' = Rotate(B'', 90.0*°, A)
poly1, b, b', b'', b''' = Polygon(B, B', B'', B''')
C = Point(b')
d = Circle(B', C)
D = Intersect(d, b)
e = Line(D, b')
f = Line(C, b)
E = Intersect(e, f)
poly2, b''_1, c_1, e_1, b'''_1 = Polygon(B'', C, E, B''')
poly3, e_2, d_1, b_1, b'''_2 = Polygon(E, D, B, B''')
poly4, c_2, b'_1, d_2, e_3 = Polygon(C, B', D, E)
g = Line(B'', f)
h = Circle(C, Zoom / 8.0)
k = Circle(B, Zoom / 8.0)
p = Circle(B'', Zoom / 8.0)
q = Circle(B''', Zoom / 8.0)
i = Line(B, f)
F, G = Intersect(k, i)
H, I = Intersect(q, g)
j = Line(B''', b')
l = Line(B'', B')
r = Circle(B', Zoom / 8.0)
J, K = Intersect(r, l)
L, M = Intersect(k, j)
N, O = Intersect(q, j)
P = Intersect(g, l)
Q, R = Intersect(p, l)
S, T = Intersect(p, g)
U, V = Intersect(h, f)
s = Circle(D, Zoom / 8.0)
W, Z = Intersect(s, e)
A_1, B_1 = Intersect(r, i)
C_1 = Midpoint(Q, O)
D_1 = Midpoint(H, F)
E_1 = Midpoint(L, W)
F_1 = Midpoint(W, K)
G_1 = Midpoint(B_1, V)
H_1 = Midpoint(V, T)
u = Vector(H_1, V)
w = Vector(G_1, B_1)
z = Vector(G_1, V)
m = Vector(F_1, K)
v_1 = Vector(D_1, F)
u_1 = Vector(E_1, L)
w_1 = Vector(D_1, H)
z_1 = Vector(C_1, Q)
v = Vector(H_1, T)
n = Vector(F_1, W)
t_2 = Vector(E_1, W)
a_1 = Vector(C_1, O)
g_1 = Line(A, xAxis)
f_1 = Circle(A, If[Animación < o, Animación, o])
I_1, J_1 = Intersect(f_1, g_1)
h_1 = Circle(J_1, If[Animación < o, Animación / 3.0, o / 3.0])
K_1, L_1 = Intersect(h_1, f_1)
i_1 = Vector(A, L_1)
j_1 = Vector(A, K_1)
B'_1 = Translate(B, i_1)
B''_1 = Translate(B', i_1)
B'''_1 = Translate(B'', i_1)
M_1 = Translate(B''', i_1)
poly1', b'_2, b''_2, b'''_3, m_1 = Polygon(B'_1, B''_1, B'''_1, M_1)
E' = Translate(E, j_1)
D' = Translate(D, j_1)
B'_2 = Translate(B, j_1)
O_1 = Translate(B''', j_1)
poly3', e', d', b'_3, o_1 = Polygon(E', D', B'_2, O_1)
k_1 = Circle(A, If[Animación < o + 4.5, Animación, o + 4.5])
S_1 = Midpoint(L_1, K_1)
T_1 = Midpoint(L_1, S_1)
a_2 = Line(A, T_1)
U_1, V_1 = Intersect(k_1, a_2)
r_1 = Vector(E, V_1)
C' = Translate(C, r_1)
B''_2 = Translate(B', r_1)
D'_1 = Translate(D, r_1)
E'_1 = Translate(E, r_1)
poly4', c', b''_3, d'_1, e'_1 = Polygon(C', B''_2, D'_1, E'_1)
E'' = Rotate(E', If[Animación < 9.0, 0.0, If[Animación < 12.14, Animación - 9.0, 3.1400000000000006]], D')
P_1 = Rotate(O_1, If[Animación < 9.0, 0.0, If[Animación ≥ 12.14, 3.1400000000000006, Animación - 9.0]], B'_2)
poly5, d'_2, e'', p_1, b'_4 = Polygon(D', E'', P_1, B'_2)
Q_1 = (14.412345276872967, -2.889850162866452)
q_1 = Circle(B''_1, Zoom / 8.0)
s_1 = Circle(B'''_1, Zoom / 8.0)
t_1 = Circle(B''_2, Zoom / 8.0)
f_2 = Circle(C', Zoom / 8.0)
R_1 = Midpoint(B''_1, B'_1)
W_1 = Midpoint(B''_2, E'_1)
l_1 = Line(R_1, g_1)
N_1 = Intersect(l_1, e'_1)
Z_1 = Midpoint(R_1, N_1)
g_2 = Circle(E'', Zoom / 8.0)
h_2 = Circle(E', Zoom / 8.0)
k_2 = Circle(D', Zoom / 8.0)
p_2 = Circle(O_1, Zoom / 8.0)
q_2 = Circle(P_1, Zoom / 8.0)
r_2 = Circle(B'_2, Zoom / 8.0)
s_2 = Circle(M_1, Zoom / 8.0)
c_3 = Circle(D'_1, Zoom / 8.0)
n_1 = Line(M_1, B'''_1)
b_2 = Line(B''_1, B'_1)
A_2, B_2 = Intersect(s_1, n_1)
C_2, D_2 = Intersect(q_1, b_2)
E_2 = Midpoint(B_2, C_2)
i_2 = Line(B'''_1, l_1)
j_2 = Line(M_1, g_1)
l_2 = Line(E', n_1)
m_2 = Line(E'', b_2)
n_2 = Line(P_1, m_2)
a_3 = Line(O_1, n_1)
b_3 = Line(D', b_2)
u_2 = Vector(E_2, C_2)
v_2 = Vector(E_2, B_2)
F_2, G_2 = Intersect(s_1, i_2)
H_2, I_2 = Intersect(s_2, j_2)
d_3 = Line(B''_2, n_2)
f_3 = Line(C', m_2)
J_2, K_2 = Intersect(f_2, f_3)
L_2, M_2 = Intersect(t_1, d_3)
g_3 = Line(D'_1, l_1)
h_3 = Line(B''_2, l_1)
N_2, O_2 = Intersect(t_1, h_3)
P_2, Q_2 = Intersect(c_3, g_3)
R_2, S_2 = Intersect(g_2, m_2)
T_2, U_2 = Intersect(h_2, l_2)
V_2, W_2 = Intersect(p_2, a_3)
Z_2, A_3 = Intersect(r_2, b_3)
B_3, C_3 = Intersect(k_2, b_3)
D_3, E_3 = Intersect(q_2, n_2)
F_3 = Intersect(k_2, d'_2)
G_3 = Intersect(r_2, p_1)
J_3 = Midpoint(J_2, L_2)
K_3 = Midpoint(O_2, Q_2)
H_3 = Midpoint(F_2, H_2)
w_2 = Vector(H_3, F_2)
z_2 = Vector(H_3, H_2)
I_3 = Midpoint(U_2, B_3)
L_3 = Midpoint(B_3, R_2)
M_3 = Midpoint(V_2, A_3)
N_3 = Midpoint(A_3, E_3)
O_3 = Midpoint(G_3, F_3)
u_3 = Vector(M_3, A_3)
v_3 = Vector(M_3, V_2)
w_3 = Vector(N_3, E_3)
z_3 = Vector(N_3, A_3)
i_3 = Vector(L_3, R_2)
j_3 = Vector(L_3, B_3)
k_3 = Vector(I_3, B_3)
m_3 = Vector(O_3, F_3)
n_3 = Vector(O_3, G_3)
p_3 = Vector(J_3, L_2)
q_3 = Vector(J_3, J_2)
r_3 = Vector(K_3, O_2)
s_3 = Vector(K_3, Q_2)
l_3 = Vector(I_3, U_2)
P_3 = Midpoint(R_1, Z_1)
Q_3 = Midpoint(Z_1, N_1)
R_3 = Midpoint(P_3, Z_1)
S_3 = Midpoint(Z_1, Q_3)
t_3 = Segment(R_3, S_3)