Pythaogoras Zerlegungsbeweis
Author: Prof. Dr. Dörte Haftendorn

Schritt 3 Beweis

Ha 08

CZ=MB=SW 
wegen Parallelverschiebung

Damit ist AC=WZ und
innen ist b^2 übrig.

A = (-0.28777777777777835, 0.881111111111111)
C = (0.2628270073557853, 2.404436360820749)
a = Segment(C, A)
b = OrthogonalLine(C, a)
B = Point(b)
poly1, c, d, e, f, D, E = Polygon(B, A, 4)
poly2, g, h, i, j, F, G = Polygon(C, B, 4)
poly3, k, l, m, n, H, I = Polygon(A, C, 4)
M = Midpoint(C, F)
p = OrthogonalLine(M, c)
q = OrthogonalLine(M, p)
J = Intersect(q, j)
K = Intersect(p, i)
L = Intersect(q, h)
N = Intersect(p, g)
O = Midpoint(c)
P = Midpoint(f)
Q = Midpoint(d)
R = Midpoint(e)
r = Line(M, A)
s = Line(M, D)
t = Line(M, B)
a1 = Line(M, E)
S = Point(r)
T = Point(s)
U = Point(a1)
V = Point(t)
u = Vector(M, S)
v = Vector(M, T)
w = Vector(M, U)
z = Vector(M, V)
poly4, m_1, n_1, b_1, l_1 = Polygon(M, N, B, L)
poly5, m_2, l_2, f_1, k_1 = Polygon(M, L, F, K)
poly6, m_3, k_2, g_1, j_1 = Polygon(M, K, G, J)
poly7, m_4, j_2, c_1, n_2 = Polygon(M, J, C, N)
M' = Translate(M, u)
N' = Translate(N, u)
B' = Translate(B, u)
L' = Translate(L, u)
poly4', m', n', b', l' = Polygon(M', N', B', L')
M'_1 = Translate(M, v)
L'_1 = Translate(L, v)
F' = Translate(F, v)
K' = Translate(K, v)
poly5', m'_1, l'_1, f', k' = Polygon(M'_1, L'_1, F', K')
M'_2 = Translate(M, z)
K'_1 = Translate(K, z)
G' = Translate(G, z)
J' = Translate(J, z)
M'_3 = Translate(M, w)
J'_1 = Translate(J, w)
C' = Translate(C, w)
N'_1 = Translate(N, w)
M'_4 = Translate(M, w)
K'_2 = Translate(K, w)
G'_1 = Translate(G, w)
J'_2 = Translate(J, w)
poly6', m'_4, k'_2, g'_1, j'_2 = Polygon(M'_4, K'_2, G'_1, J'_2)
M'_5 = Translate(M, z)
J'_3 = Translate(J, z)
C'_1 = Translate(C, z)
N'_2 = Translate(N, z)
poly7', m'_5, j'_3, c'_1, n'_2 = Polygon(M'_5, J'_3, C'_1, N'_2)
W = Translate(S, z)
u1 = Vector(S, W)
Z = Translate(C, z)
v1 = Vector(C, Z)
poly8, n'_1, s_1, w_1 = Polygon(S, W, N')