Pythagoräischer Lehrsatz: Schiebebeweis

Beschreibe mit eigenen Worten, was bei den zwei Phasen passiert.

A = (-4.560189183673528, 1.150187209741187)
B = (0.2690667025311159, -0.3372236032098434)
c = Semicircle(A, B)
C = Point(c)
Vieleck1, b, a, c_1 = Polygon(A, C, B)
A'_1 = Rotate(A, 270*°, C)
C'_1 = Rotate(C, 270*°, C)
B'_1 = Rotate(B, 270*°, C)
Vieleck1'_1, b', a', c' = Polygon(A'_1, C'_1, B'_1)
d = Line(C, B'_1)
e = Circle(C, Segment[B'_1, A])
D = Intersect(e, d, 1)
u = Vector(C, D)
Phase_1 = 1 (slider from 0 to 1, step 0.01)
A''_1 = Translate(A'_1, Vector[(Phase_1 * u)])
C''_1 = Translate(C'_1, Vector[(Phase_1 * u)])
B''_1 = Translate(B'_1, Vector[(Phase_1 * u)])
Vieleck1''_1, b'', a'', c'' = Polygon(A''_1, C''_1, B''_1)
A'''_1 = Rotate(A''_1, 270*°, C)
C'''_1 = Rotate(C''_1, 270*°, C)
B'''_1 = Rotate(B''_1, 270*°, C)
Vieleck1'''_1, b''', a''', c''' = Polygon(A'''_1, C'''_1, B'''_1)
f = OrthogonalLine(D, u)
g = Circle(D, C)
E = Intersect(g, f, 1)
v = Vector(D, E)
F = Translate(A'''_1, Vector[(Phase_1 * u)])
G = Translate(C'''_1, Vector[(Phase_1 * u)])
H = Translate(B'''_1, Vector[(Phase_1 * u)])
Vieleck2, h, f_1, g_1 = Polygon(F, G, H)
F' = Rotate(F, 270*°, G)
G' = Rotate(G, 270*°, G)
H' = Rotate(H, 270*°, G)
Vieleck2', h', f', g' = Polygon(F', G', H')
F'' = Translate(F', Vector[((-Phase_1) * u)])
G'' = Translate(G', Vector[((-Phase_1) * u)])
H'' = Translate(H', Vector[((-Phase_1) * u)])
Vieleck2'', h'', f'', g'' = Polygon(F'', G'', H'')
w: u + v
I = Translate(A'''_1, w)
J = Translate(C'''_1, w)
K = Translate(B'''_1, w)
Vieleck3, k, i, j = Polygon(I, J, K)
Phase_2 = 0 (slider from 0 to 1, step 0.01)
winkel = 4.71238898038469 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
L = (3.668862846419186, 1.1115531626515498)
z = Vector(A, L)
A' = Translate(A, z)
C' = Translate(C, z)
B' = Translate(B, z)
Vieleck1', b'_1, a'_1, c'_1 = Polygon(A', C', B')
A'' = Rotate(A', 270*°, C')
C'' = Rotate(C', 270*°, C')
B'' = Rotate(B', 270*°, C')
Vieleck1'', b''_1, a''_1, c''_1 = Polygon(A'', C'', B'')
A''' = Translate(A'', u)
C''' = Translate(C'', u)
B''' = Translate(B'', u)
Vieleck1''', b'''_1, a'''_1, c'''_1 = Polygon(A''', C''', B''')
M = Rotate(A''', 270*°, C''')
N = Rotate(C''', 270*°, C''')
O = Rotate(B''', 270*°, C''')
Vieleck4, o, m, n = Polygon(M, N, O)
M' = Translate(M, v)
N' = Translate(N, v)
O' = Translate(O, v)
Vieleck4', o', m', n' = Polygon(M', N', O')
M''_1 = Rotate(M', 270*°, N')
N''_1 = Rotate(N', 270*°, N')
O''_1 = Rotate(O', 270*°, N')
Vieleck4''_1, o'', m'', n'' = Polygon(M''_1, N''_1, O''_1)
M''' = Translate(M''_1, Vector[(-u)])
N''' = Translate(N''_1, Vector[(-u)])
O''' = Translate(O''_1, Vector[(-u)])
Vieleck4''', o''', m''', n''' = Polygon(M''', N''', O''')
M'' = Rotate(M', (Phase_2 * winkel), A''')
N'' = Rotate(N', (Phase_2 * winkel), A''')
O'' = Rotate(O', (Phase_2 * winkel), A''')
Vieleck4'', o''_1, m''_1, n''_1 = Polygon(M'', N'', O'')
Vieleck5, c'_2, n'''_1, n'_1, c'''_2 = Polygon(C', N''', N', C''')
Vieleck6, c_2, g''_1, g_2, c''_2 = Polygon(C, G'', G, C''_1)
P = Rotate(M''', (-((Phase_2 * winkel))), B')
Q = Rotate(N''', (-((Phase_2 * winkel))), B')
R = Rotate(O''', (-((Phase_2 * winkel))), B')
Vieleck7, r, p, q = Polygon(P, Q, R)
l = Line(N', N''')
S = Intersect(p, l)
Vieleck8, s, n'_2, t, a_1, T, U = Polygon(S, N', 4)
Vieleck9, n'''_2, s_1, b_1, d_1, V, W = Polygon(N''', S, 4)
Vieleck10, a_2, b_2, e_1, h_1, Z, A_1 = Polygon(A, B, 4)