β

γ

α

Οι διακεκομένες γραμμές 
που χωρίζουν το Εγ,
είναι παράλληλλες με τις 
πλευρές του τετραγώνου
της υποτείνουσας.
Μπορείς να αλλάξεις τον
χωρισμό μετακινόντας τις
κίτρινες κουκίδες.

Να μεταφέρεις τα 
χρωματιστά κομμάτια 
ώστε να γεμίσεις το 
άδειο τετράγωνο της 
υποτείνουσας.

Τα χρωματιστά κομμάτια 
μεταφέρονται πιάνοντάς τα
από τις αντίστοιχες χρωματιστές
κουκίδες.

Τι συμπέρασμα βγάζεις;

Οπτική απόδειξη του Πυθαγορείου θεωρήματος

A = (-1.9027174941344192, -2.789198931406712)
B = (9.366700884451694, -2.8428628284475983)
c = Semicircle(A, B)
a = Segment(A, B)
C = Point(c)
b = Segment(C, A)
d = Segment(C, B)
Ε_β, a_1, c_1, e, f, D, E = Polygon(A, C, 4)
E_γ, c_2, b_1, g, h, F, G = Polygon(C, B, 4)
Ε_α, b_2, a_2, i, j, H, I = Polygon(B, A, 4)
k = OrthogonalLine(G, a)
l = OrthogonalLine(B, a)
m = Line(F, a)
n = Line(C, a)
J = Intersect(k, n)
K = Intersect(l, n)
p = Segment(J, K)
L = Intersect(k, m)
q = Segment(J, L)
M = Point(p)
N = Point(q)
r = OrthogonalLine(M, p)
s = OrthogonalLine(N, q)
O = Intersect(r, s)
P = Intersect(s, b_1)
Q = Intersect(r, g)
R = Intersect(s, h)
S = Intersect(r, c_2)
T = (6, 8)
U = (9.995558097931886, 6.618350956414503)
V = (9.061746434238515, 0.4748531689581238)
W = (5.375647761764688, 0.7205930804563789)
Z = (-2.438881423879826, -0.36066253013594374)
u = Vector(Z, D)
v = Vector(Z, C)
w = Vector(Z, A)
z = Vector(Z, E)
t = Vector(W, C)
u_1 = Vector(W, R)
v_1 = Vector(W, O)
w_1 = Vector(W, S)
z_1 = Vector(T, R)
d_1 = Vector(T, O)
e_1 = Vector(T, Q)
f_1 = Vector(T, G)
g_1 = Vector(U, Q)
h_1 = Vector(U, O)
i_1 = Vector(U, P)
j_1 = Vector(U, F)
k_1 = Vector(V, O)
l_1 = Vector(V, S)
m_1 = Vector(V, B)
n_1 = Vector(V, P)
A_1 = (9.916921326252403, 6.534799386505097)
B_1 = (5.9162755670608265, 8.048557241334349)
C_1 = (5.321584981235051, 0.7500818698361732)
D_1 = (9.051916837778549, 0.5338307477177088)
E_1 = Translate(B_1, f_1)
p_1 = Vector(B_1, E_1)
F_1 = Translate(B_1, e_1)
q_1 = Vector(B_1, F_1)
G_1 = Translate(B_1, z_1)
r_1 = Vector(B_1, G_1)
H_1 = Translate(B_1, d_1)
s_1 = Vector(B_1, H_1)
I_1 = Translate(A_1, g_1)
t_1 = Vector(A_1, I_1)
J_1 = Translate(A_1, h_1)
u_2 = Vector(A_1, J_1)
K_1 = Translate(A_1, j_1)
v_2 = Vector(A_1, K_1)
L_1 = Translate(A_1, i_1)
w_2 = Vector(A_1, L_1)
M_1 = Translate(C_1, v_1)
z_2 = Vector(C_1, M_1)
N_1 = Translate(C_1, u_1)
d_2 = Vector(C_1, N_1)
O_1 = Translate(C_1, t)
e_2 = Vector(C_1, O_1)
P_1 = Translate(C_1, w_1)
f_2 = Vector(C_1, P_1)
Q_1 = Translate(D_1, k_1)
g_2 = Vector(D_1, Q_1)
R_1 = Translate(D_1, l_1)
h_2 = Vector(D_1, R_1)
S_1 = Translate(D_1, m_1)
i_2 = Vector(D_1, S_1)
T_1 = Translate(D_1, n_1)
j_2 = Vector(D_1, T_1)
U_1 = (-2.463455415029639, -0.3311737407561491)
V_1 = Translate(U_1, w)
k_2 = Vector(U_1, V_1)
W_1 = Translate(U_1, z)
l_2 = Vector(U_1, W_1)
Z_1 = Translate(U_1, u)
m_2 = Vector(U_1, Z_1)
A_2 = Translate(U_1, v)
n_2 = Vector(U_1, A_2)
πολύγ.4, z_3, w_3, v_3, a_3 = Polygon(Z_1, W_1, V_1, A_2)
πολύγ.5, g_3, h_3, f_3, e_3 = Polygon(G_1, H_1, F_1, E_1)
πολύγ.6, i_3, j_3, l_3, k_3 = Polygon(I_1, J_1, L_1, K_1)
πολύγ.7, q_2, t_2, s_2, r_2 = Polygon(Q_1, T_1, S_1, R_1)
πολύγ.8, m_3, p_2, o_1, n_3 = Polygon(M_1, P_1, O_1, N_1)
b_3 = Segment(Q, S)
c_3 = Segment(R, P)
d_3 = Segment(C, A)
p_3 = Segment(C, B)
q_3 = Segment(B, A)
α = Angle(A, C, B)