PairOfAngledMirrors

Move

Move

Move

Result

Angle Size

2nd Reflection

1st Reflection

A = (-7.971917580366586, 4.226010213915615)
B = (-8.067783179019752, 0.4153526674521806)
C = (-6.294269603936129, 0.4393190671154721)
D = (-6.677731998548806, 2.5004294381585876)
E = (-5.23974801875128, 2.716127035128216)
F = (-5.335613617404448, 4.561539809201703)
poly1, a, b, c, d, e, f = Polygon(A, B, C, D, E, F)
g = Segment(A, F)
h = Segment(F, E)
i = Segment(E, D)
j = Segment(D, C)
k = Segment(C, B)
l = Segment(B, A)
G = (-7.013114800197296, 8.748443853791219)
n = Line(G, m)
H = Point(n)
p = Circle(G, H)
I = Point(p)
α_1 = 3.14
q = CircleSector(G, H, I)
J = (0.670791455194453, 8.750334399852584)
r = Circle(H, G)
K = Intersect(r, n, 2)
L = Midpoint(H, K)
H' = Mirror(H, K)
L' = Mirror(L, K)
s = Circle(L', L)
M = Intersect(s, n, 2)
N = Point(s)
β = Angle(M, L', N)
t = CircleSector(L', M, N)
α = Angle(H, G, I)
A' = Rotate(A, α, J)
B' = Rotate(B, α, J)
C' = Rotate(C, α, J)
D' = Rotate(D, α, J)
E' = Rotate(E, α, J)
F' = Rotate(F, α, J)
poly1', a', b', c', d', e', f' = Polygon(A', B', C', D', E', F')
A'_1 = Rotate(A, α, J)
F'_1 = Rotate(F, α, J)
g' = Segment(A'_1, F'_1)
F'_2 = Rotate(F, α, J)
E'_1 = Rotate(E, α, J)
h' = Segment(F'_2, E'_1)
E'_2 = Rotate(E, α, J)
D'_1 = Rotate(D, α, J)
i' = Segment(E'_2, D'_1)
D'_2 = Rotate(D, α, J)
C'_1 = Rotate(C, α, J)
j' = Segment(D'_2, C'_1)
C'_2 = Rotate(C, α, J)
B'_1 = Rotate(B, α, J)
k' = Segment(C'_2, B'_1)
B'_2 = Rotate(B, α, J)
A'_2 = Rotate(A, α, J)
l' = Segment(B'_2, A'_2)
c_1 = Circle(J, 1.5)
O = Point(c_1)
O' = Rotate(O, β, J)
a_1 = Line(O, J)
b_1 = Line(J, O')
d_1 = Segment(F, J)
e_1 = Segment(J, F'_2)
γ = Angle(F, J, F'_2)
δ = Angle(O, J, O')
f_1 = CircleSector(J, O, O')
A'_3 = Mirror(A, a_1)
B'_3 = Mirror(B, a_1)
C'_3 = Mirror(C, a_1)
D'_3 = Mirror(D, a_1)
E'_3 = Mirror(E, a_1)
F'_3 = Mirror(F, a_1)
poly1'_1, a'_3, b'_3, c'_3, d'_3, e'_3, f'_3 = Polygon(A'_3, B'_3, C'_3, D'_3, E'_3, F'_3)
A'_4 = Mirror(A, a_1)
F'_4 = Mirror(F, a_1)
g'_1 = Segment(A'_4, F'_4)
F'_5 = Mirror(F, a_1)
E'_4 = Mirror(E, a_1)
h'_1 = Segment(F'_5, E'_4)
E'_5 = Mirror(E, a_1)
D'_4 = Mirror(D, a_1)
i'_1 = Segment(E'_5, D'_4)
D'_5 = Mirror(D, a_1)
C'_4 = Mirror(C, a_1)
j'_1 = Segment(D'_5, C'_4)
C'_5 = Mirror(C, a_1)
B'_4 = Mirror(B, a_1)
k'_1 = Segment(C'_5, B'_4)
B'_5 = Mirror(B, a_1)
A'_5 = Mirror(A, a_1)
l'_1 = Segment(B'_5, A'_5)
P = Mirror(A'_3, b_1)
Q = Mirror(B'_3, b_1)
R = Mirror(C'_3, b_1)
S = Mirror(D'_3, b_1)
T = Mirror(E'_3, b_1)
U = Mirror(F'_3, b_1)
poly2, p_1, q_1, r_1, s_1, t_1, u = Polygon(P, Q, R, S, T, U)
V = Mirror(A'_3, b_1)
W = Mirror(B'_3, b_1)
g_1 = Segment(V, W)
Z = Mirror(B'_3, b_1)
A_1 = Mirror(C'_3, b_1)
h_1 = Segment(Z, A_1)
B_1 = Mirror(C'_3, b_1)
C_1 = Mirror(D'_3, b_1)
i_1 = Segment(B_1, C_1)
D_1 = Mirror(D'_3, b_1)
E_1 = Mirror(E'_3, b_1)
j_1 = Segment(D_1, E_1)
F_1 = Mirror(E'_3, b_1)
G_1 = Mirror(F'_3, b_1)
k_1 = Segment(F_1, G_1)
H_1 = Mirror(F'_3, b_1)
I_1 = Mirror(A'_3, b_1)
l_1 = Segment(H_1, I_1)
J_1 = Mirror(A'_4, b_1)
K_1 = Mirror(F'_4, b_1)
m_1 = Segment(J_1, K_1)
L_1 = Mirror(A'_4, b_1)
M_1 = Mirror(F'_4, b_1)
N_1 = Mirror(F'_5, b_1)
O_1 = Mirror(E'_4, b_1)
n_1 = Segment(N_1, O_1)
P_1 = Mirror(F'_5, b_1)
Q_1 = Mirror(E'_4, b_1)
R_1 = Mirror(E'_5, b_1)
S_1 = Mirror(D'_4, b_1)
a_2 = Segment(R_1, S_1)
T_1 = Mirror(E'_5, b_1)
U_1 = Mirror(D'_4, b_1)
V_1 = Mirror(D'_5, b_1)
W_1 = Mirror(C'_4, b_1)
b_2 = Segment(V_1, W_1)
Z_1 = Mirror(D'_5, b_1)
A_2 = Mirror(C'_4, b_1)
B_2 = Mirror(C'_5, b_1)
C_2 = Mirror(B'_4, b_1)
c_2 = Segment(B_2, C_2)
D_2 = Mirror(C'_5, b_1)
E_2 = Mirror(B'_4, b_1)
F_2 = Mirror(B'_5, b_1)
G_2 = Mirror(A'_5, b_1)
d_2 = Segment(F_2, G_2)
H_2 = Mirror(B'_5, b_1)
I_2 = Mirror(A'_5, b_1)
e_2 = Segment(L', M)
J_2 = Point(e_2)
f_2 = Segment(J_2, N)
g_2 = Segment(J, O')
h_2 = Segment(J, O)
K_2 = Point(d_1)
text1: "$ \alpha = " + (LaTeX[α]) + " $"
text2: "$ \beta = " + (LaTeX[β]) + " $"
ab: α / β
text3: "$ \alpha : \beta =" + (LaTeX[α]) + ": " + (LaTeX[β]) + " = " + (LaTeX[ab]) + ":1$"
o = false
v = false
w = false
z = false
k_2 = Circle(J, O')
L_2 = Intersect(k_2, d_1)
M_2 = Midpoint(J, L_2)
N_2 = Midpoint(M_2, L_2)
O_2 = Midpoint(L_2, N_2)
p_2 = Circle(J, O_2)
r_2 = Circle(J, O_2)
Q_2 = Intersect(r_2, e_1)
q_2 = CircleSector(J, O_2, Q_2)

Tool: Complex Multiplication (command ComplexMultiplication)
Select Points at O(0, 0), P(0, -1), A and B for A*B
Input: O, P, A, B
Output: j, AB

c = Circle(O, A)
d = Circle(O, B)
D = Intersect(c, xAxis, 2)
b = Segment(O, A)
f = Segment(O, B)
G = Intersect(d, xAxis, 1)
g = Circle(D, P, G)
E = Intersect(g, yAxis, 2)
e = Circle(O, E)
a, h = AngularBisector(f, b)
D' = Mirror(D, a)
i = Ray(O, D')
AB = Intersect(e, i, 1)
j = Segment(O, AB)

Tool: Complex Division (command ComplexDivision)
Select Points O(0, 0), P(0, -1), A and B for A/B
Input: O, P, A, B
Output: l, C

A/B

c = Circle(O, A)
d = Circle(O, B)
D = Intersect(c, xAxis, 2)
e = AngularBisector(A, O, D)
B' = Mirror(B, e)
f = Ray(O, B')
E = Intersect(c, yAxis, 1)
F = Intersect(d, xAxis, 1)
g = Segment(F, E)
G = Midpoint(g)
h = OrthogonalLine(G, g)
i = Segment(P, F)
H = Midpoint(i)
j = OrthogonalLine(H, i)
I = Intersect(h, j)
k = Circle(I, F)
J = Intersect(k, xAxis, 2)
p = Circle(O, J)
C = Intersect(p, f)
l = Segment(O, C)

Tool: Complex Addition (command ComplexAddition)
Select Points O(0, 0), A and B for A + B
Input: O, A, B
Output: C', c

A + B

u = Vector(O, B)
C' = Translate(A, u)
c = Segment(O, C')

Tool: Complex Subtraction (command ComplexSubtraction)
Select Points O(0, 0), A and B for A - B
Input: O, A, B
Output: c, A'

A - B

u = Vector(B, O)
A'_1 = Translate(A, u)
A' = Translate(A, u)
c = Segment(O, A')