A

Il teorema di Pitagora in relazione ai due teoremi di Euclide    ( puoi muovere il punto A )

1° teorema di Euclide :   Q_a = a ² = c · c_a  ,   Q_b = b ² = c · c_b
quindi :    Q_a + Q_b = c ( c_a + c_b ) = c ² = Q_c

2° teorema di Euclide :   h ²  = ( a + m ) m = a m + m ²
quindi ( BD = c ) :   Q_b = 4 h ² = 4 a m + 4 m ² = 4 R + 4 Q = Q_c - Q_a

R

R

R

Q

Q

Q

Q_a

Q_b

muovi = (2.4067247530739775, 3.019164941085923)
B_2 = If(x(muovi) > 0.0 ∧ y(muovi) > 0.0, muovi)
a_1 = Line(B_2, yAxis)
C = Intersect(a_1, xAxis)
B = (0, 0)
c = Segment(B_2, B)
a = Segment(B, C)
b = Segment(C, B_2)
d_2 = Circle(B, B_2)
D = Intersect(d_2, xAxis, 2.0)
e = Segment(C, D)
f = Segment(B_2, D)
poli1, b_1, a_2, c_1 = Polygon(B, C, B_2)
Q_c, s, t, d_1, e_1, F, I = Polygon(B, B_2, 4.0)
Q_b, d, i, j, k, D_1, E = Polygon(B_2, C, 4.0)
Q_a, m_1, n, q, r, G, H = Polygon(C, B, 4.0)
α = Angle(B_2, C, B)
l = Segment(B_2, D)
M = Midpoint(l)
p = Segment(B, M)
J = Midpoint(d)
K = Midpoint(j)
L = Midpoint(k)
N = Midpoint(i)
g = Segment(J, K)
h_1 = Segment(N, L)
M': (x(M), 0.0)
h = Segment(M, M')
m = Segment(C, M')
O: (0.0, -x(D))
P: (x(D), -x(D))
β = Angle(B, M, D)
Q_1: (x(M'), -x(M'))
R_1: (x(M'), y(H))
S: (x(D), y(H))
T: (x(C), -x(M'))
U: (x(C), -x(D))
V: (x(M'), -x(D))
W: (x(D), -x(M'))
R, c_2, h_2, r_1, m' = Polygon(C, H, R_1, M')
poli3, m'_1, r_2, s_1, b' = Polygon(M', R_1, S, D)
Z: (0.0, -x(M'))
poli4, g_1, z, t_1, h_3 = Polygon(G, Z, T, H)
poli5, z_1, o, u, t_2 = Polygon(Z, O, U, T)
poli6, u_1, v, q_1, t_3 = Polygon(U, V, Q_1, T)
poli7, v_1, p_1, w, q_2 = Polygon(V, P, W, Q_1)
Q, t_4, q_3, r_3, h_4 = Polygon(T, Q_1, R_1, H)
poli9, q_4, w_1, s_2, r_4 = Polygon(Q_1, W, S, R_1)
f_1 = OrthogonalLine(C, c)
A_1 = Intersect(f_1, d_1)
B_1 = Intersect(f_1, c)
i_1 = Segment(C, B_1)
poli2, i_2, a_3, b_2, a_4 = Polygon(I, B, B_1, A_1)
poli8, a_5, b_3, muovi_1, f_2 = Polygon(A_1, B_1, muovi, F)
γ = Angle(C, B_1, muovi)
c_b = Segment(muovi, B_1)
c_a = Segment(B_1, B)