grün + blau =  rot

Dreieck und Parallelogramme

Höhengleis

Mit den (drei) Schiebereglern wird gezeigt,
dass das blaue und grüne Parallelogramm
zusammen das rote Parallelogramm ergeben.

A = (1.82, -2.24)
B = (7.4, -1.52)
C = (3.22, 0.94)
Vieleck1, c_3, a, b = Polygon(A, B, C)
D = (-1.02, -2.2)
E = (9.22, 0.16)
d = Line(D, A)
e = Line(E, B)
f = Line(D, b)
g = Line(C, d)
h = Line(E, a)
i = Line(C, e)
F = Intersect(f, h)
j = Segment(C, F)
G = Intersect(f, g)
H = Intersect(h, i)
Vieleck2, d_1, a_1, c_1, g_1 = Polygon(D, A, C, G)
Vieleck3, c_2, b_1, e_1, h_1 = Polygon(C, B, E, H)
k = Line(A, j)
I = Intersect(f, k)
l = Line(B, j)
J = Intersect(l, h)
m_3 = Segment(D, I)
n = Segment(E, J)
phase_1 = 0 (slider from 0 to 1, step 0.01)
P_1: D + (phase_1 * (I - D))
p = Line(A, P_1)
q = Line(C, p)
K = Intersect(f, q)
Vieleck4, p_1, a_2, c_4, k_1 = Polygon(P_1, A, C, K)
r = Segment(D, F)
Vieleck5, i_1, a_3, c_5, f_1 = Polygon(I, A, C, F)
P_2: E + (phase_1 * (J - E))
s = Line(P_2, B)
t = Line(C, s)
L = Intersect(h, t)
Vieleck6, b_2, p_2, l_1, c_6 = Polygon(B, P_2, L, C)
Vieleck7, c_7, b_3, j_1, f_2 = Polygon(C, B, J, F)
v_1: C - F
phase_2 = 0 (slider from 0 to 1, step 0.01)
I' = Translate(I, Vector[(phase_2 * v_1)])
A' = Translate(A, Vector[(phase_2 * v_1)])
C' = Translate(C, Vector[(phase_2 * v_1)])
F' = Translate(F, Vector[(phase_2 * v_1)])
Vieleck5', i', a', c', f' = Polygon(I', A', C', F')
C'_1 = Translate(C, Vector[(phase_2 * v_1)])
B' = Translate(B, Vector[(phase_2 * v_1)])
J' = Translate(J, Vector[(phase_2 * v_1)])
F'_1 = Translate(F, Vector[(phase_2 * v_1)])
Vieleck7', c'_1, b', j', f'_1 = Polygon(C'_1, B', J', F'_1)
m_1 = Segment(B, E)
n_1 = Segment(A, D)
q_1 = Line(F, C)
r_1 = Circle(A, I)
M = Intersect(r_1, k, 2)
s_1 = Line(M, c_3)
N = Intersect(l, s_1)
Vieleck8, a_4, m_2, n_2, b_4 = Polygon(A, M, N, B)
O = Intersect(q_1, m_2)
t_1 = Circle(C, Segment[A, M])
P = Intersect(t_1, q_1, 2)
phase_3 = 0 (slider from 0 to 1, step 0.01)
P_3: P + (phase_3 * (O - P))
d_2 = Line(M, P_3)
e_2 = Line(A, d_2)
Q = Intersect(q_1, e_2)
Vieleck9, m_4, p_3, q_2, a_5 = Polygon(M, P_3, Q, A)
Vieleck10, n_3, b_5, q_3, p_4 = Polygon(N, B, Q, P_3)
g_2 = Segment(A', B')
R = (-9.550666666666672, -3.2293333333333347)
S = Point(Circle[R, c_3])
T = Rotate(S + (a, 0), Angle[C - B] + Angle[S - R] - Angle[B - A], S)
u = Vector(A, R)
D' = Translate(D, u)
E' = Translate(E, u)
A'' = Translate(M, u)
B'' = Translate(N, u)
U = (14.96, -2.34)
V = Point(Circle[U, a_4])
W = Rotate(V + (m_2, 0), Angle[N - M] + Angle[V - U] - Angle[M - A], V)
Z = Rotate(W + (n_2, 0), Angle[B - N] + Angle[W - V] - Angle[N - M], W)
A_1 = (14.76, 0.68)
B_1 = Point(Circle[A_1, c_2])
C_1 = Rotate(B_1 + (b_1, 0), Angle[E - B] + Angle[B_1 - A_1] - Angle[B - C], B_1)
D_1 = Rotate(C_1 + (e_1, 0), Angle[H - E] + Angle[C_1 - B_1] - Angle[E - B], C_1)
E_1 = (14.26, -4.46)
F_1 = Point(Circle[E_1, d_1])
G_1 = Rotate(F_1 + (a_1, 0), Angle[C - A] + Angle[F_1 - E_1] - Angle[A - D], F_1)
H_1 = Rotate(G_1 + (c_1, 0), Angle[G - C] + Angle[G_1 - F_1] - Angle[C - A], G_1)
I_1 = (20.52, -1.6)
c = Vector(B, I_1)
A'_1 = Translate(A, c)
B'_1 = Translate(B, c)
C'_2 = Translate(C, c)
m = false