Teorema di Pitagora
Author: Damiano Patrese
Date: 21 Maggio 2013

Dimostrazione

Ripristina

viola = 0 (slider from 0 to Length[Segment[A, J]] - Length[q], step 0.1)
β = 0 rad (slider from 0 to 180*°, step 0.017453292519943295)
B = (8, -2)
A = (-2, -2)
c = Semicircle(A, B)
C = Point(c)
poli1, a, b, d, e, F, G = Polygon(A, C, 4)
poli2, f, g, h, i, C_1, D = Polygon(A, B, 4)
v = UnitVector(Segment[D, A])
J = Intersect(i, b)
J'_1 = Rotate(J, -β, J)
F' = Rotate(F, -β, J)
G' = Rotate(G, -β, J)
poli3, j, k, l, m, H, I = Polygon(C, B, 4)
K = Intersect(m, h)
poli4, b_1, c_1, h_1 = Polygon(C_1, H, B)
poli5, c_2, k_1, i_1 = Polygon(K, I, C_1)
poli6, k_2, c_3, b_2, c_4 = Polygon(K, C_1, B, C)
poli7, a_1, j_1, c_5 = Polygon(J, C, A)
poli8, a_2, g_1, f_1, j_2 = Polygon(A, G, F, J)
α = 0 rad (slider from 0*° to 180*°, step 0.017453292519943295)
E = Rotate(C_1, α / 2, B)
H' = Rotate(H, α / 2, B)
poli9, b_3, e_1, h' = Polygon(E, H', B)
K' = Rotate(K, (-α) / 2, K)
I' = Rotate(I, (-α) / 2, K)
C'_1 = Rotate(C_1, (-α) / 2, K)
poli10, c'_1, k', i' = Polygon(K', I', C'_1)
C' = Rotate(C, α / 2, C)
J' = Rotate(J, (-α) / 2, C)
A' = Rotate(A, (-α) / 2, C)
poli11, j', c_6, a' = Polygon(C, A', J')
giallo = 0 (slider from 0 to x(K) - x(D), step 0.1)
poli12, n, p, q = Polygon(K' - giallo, I' - giallo, C'_1 - giallo)
u = UnitVector(Segment[C, K'])
azzurro = 0 (slider from 0 to Distance[J', K], step 0.1)
poli13, r, s, t = Polygon(A' + azzurro * u, J' + azzurro * u, C' + azzurro * u)
A'_1 = Rotate(A, -β, J)
poli14, d_1, l_1, m_1, n_1 = Polygon(A'_1 + viola * v, G' + viola * v, F' + viola * v, J'_1 + viola * v)
p_1 = Segment(C, A)
q_1 = Segment(C, B)
r_1 = Segment(B, A)