Identità di polarizzazione :
 
detto M il punto medio tra un punto P e l'unità, si ha :
ascissa(P) = area(quadrato(OM)) - area(quadrato(UM))

Q2

P2

Q1 - P2

P2

Q1 - P2

P2

U = (1, 0)
P = (0.4206849175021439, 0.786999390988965)
f = Segment(P, U)
M = Midpoint(f)
Q2, m_1, u, j, k, F_2, G = Polygon(M, U, 4)
p = Line(F_2, G)
R = Intersect(xAxis, p)
n_1 = Line(M, xAxis)
L = Intersect(n_1, p)
O = (0, 0)
Q1, o_1, m_2, h, i, D, E_2 = Polygon(O, M, 4)
n = Line(E_2, D)
J = Intersect(xAxis, n)
I = Intersect(n, n_1)
Q = Intersect(n, yAxis)
l = Line(M, yAxis)
T = Intersect(l, n)
a = Segment(O, P)
b = Line(P, yAxis)
X = Intersect(xAxis, b)
d = Segment(P, X)
B_2 = (0, -1)
e = Line(B_2, xAxis)
C = Intersect(e, b)
poli1, o, b_1, c_1, a_1 = Polygon(O, B_2, C, X)
g = Segment(O, M)
m: Q1 - Q2
distanzaOA = Distance(O, X)
poli4, t, h_1, i_1, l_1 = Polygon(O, M, I, J)
P2, c, g_1, j_1, k_1 = Polygon(M, U, R, L)
r = Line(Q, xAxis)
K = Intersect(l, r)
H = Intersect(xAxis, l)
e_1 = Segment(E_2, T)
f_1 = Segment(T, H)
s = Segment(Q, K)
p_1 = Line(I, f)
S_1 = Intersect(p_1, xAxis)
poli6, i_2, s_1, q_1, r_1, V_1, W_1 = Polygon(I, S_1, 4)
t_1 = Line(V_1, W_1)
Z = Intersect(t_1, n_1)
a_2 = Line(Z, n)
W = Intersect(a_2, xAxis)
b_2 = Segment(Z, W)
c_2 = Line(M, D)
B = Intersect(c_2, a_2)
V = Intersect(yAxis, a_2)
d_2 = Line(V, xAxis)
DD = Intersect(d_2, l)
poli7, j_2, w, z, i_3 = Polygon(J, W, Z, I)
poli9, e_2, g_2, h_2, k_2 = Polygon(O, H, DD, V)
l_2 = Line(H, B_2)
n_2 = Line(O, l_2)
f_2 = Line(O, E_2)
E = Intersect(f_2, a_2)
poli10, e_3, b_3, d_4, e_4 = Polygon(E, B, D, E_2)
F = Intersect(a_2, l)
poli11, c_4, f_3, t_2, q = Polygon(V, F, T, Q)
d_1 = Segment(J, T)
A = Intersect(n_2, d_2)
N = Intersect(l_2, d_2)
poli12, o_2, h_3, n_3, a_3 = Polygon(O, H, N, A)
S = Intersect(l_2, b)
poli13, b_4, s_2, a_4, o_3 = Polygon(B_2, S, A, O)
p_2 = Segment(N, B_2)
AA = Intersect(t_1, xAxis)
poli8, s_3, aa, z_1, i_4 = Polygon(S_1, AA, Z, I)
testo1: "area( q(OM) ) = area(Q1) = " + Q1 + "
area( q(UM) ) = area(Q2) = area(P2) = " + Q2 + "
area(Q1) - area(Q2) = " + m + ""