Author: 藍邦偉　老師
Date: 18 4 月 2014

$α=%v$

$β=%v$

$O$

單位向量

座標軸

x

y

z

$A_1$

$A_2$

$A_3$

$A_4$

$A_5$

$A_6$

$A_7$

$A_8$

$B_1$

$B_2$

$B_3$

$B_4$

$C_1$

$C_2$

$C_3$

$C_4$

$D_1$

$D_4$

$D_3$

$D_2$

$S_e$

$S_f$

$S_a$

$S_b$

$S_c$

$S_d$

$Step=%v$

$M_1$

$S_1$

$正十二面體的史坦納樹$

$M_2$

$S_2$

$S_1$

$S_2$

$S_3$

$S_4$

$S_5$

$S_6$

$S_b$

$S_c$

$S_d$

$S_e$

$S_f$

$S_a$

$t=%v$

t=

$t=$

O

$M_1$

$M_2$

$M_3$

$M_4$

$M_5$

$M_6$

$M_7$

$M_8$

4

切換有效小數位數

$8(\sqrt{15}-\sqrt{3})+12.392=29.519$

k_0 = 0.2593294638334492 (slider from -5 to 5, step 1)
α = 3.6302848441482056 rad (slider from 0*° to 6.283185307179586, step 0.1*°)
β = 1.3962634015954636 rad (slider from 0 to 6.283185307179586, step 0.1*°)
O = (12.401897394714963, 3.6486915472106127)
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
v = Vector(O, Y_{unit})
X_{unit}: O + (cos(α), sin(α) * cos(β))
u = Vector(O, X_{unit})
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
L = 2 (slider from 1 to 10, step 1)
yy = Vector(O - L * v, O + L * v)
zz = Vector(O - L * w, O + L * w)
xx = Vector(O - L * u, O + L * u)
y_d = false
y_e = false
Q_2: 0.33 * Corner[2] + 0.67 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
z_g = Segment(Q_2, Q_3)
poly0, z_h, q_1, q_4, z_i = Polygon(Corner[1], Q_2, Q_3, Corner[4])
φ = 1.618033988749895
A_1: O + u + v + w
A_2: O - u + v + w
A_3: O - u - v + w
A_4: O + u - v + w
A_5: O + u + v - w
A_6: O - u + v - w
A_7: O - u - v - w
A_8: O + u - v - w
B_1: O + φ * u + 1 / φ * v
B_2: O - φ * u + 1 / φ * v
B_3: O - φ * u - 1 / φ * v
B_4: O + φ * u - 1 / φ * v
C_1: O + φ * v + 1 / φ * w
C_2: O - φ * v + 1 / φ * w
C_3: O - φ * v - 1 / φ * w
C_4: O + φ * v - 1 / φ * w
D_1: O + φ * w + 1 / φ * u
D_4: O - φ * w + 1 / φ * u
D_3: O - φ * w - 1 / φ * u
D_2: O + φ * w - 1 / φ * u
S_e: O + (-1 + sqrt(3) / 3) * v
S_f: O + (1 - sqrt(3) / 3) * v
S_a: O - (1 - sqrt(3) / 6) * v + 0.5 * w
S_b: O - (1 - sqrt(3) / 6) * v - 0.5 * w
S_c: O + (1 - sqrt(3) / 6) * v + 0.5 * w
S_d: O + (1 - sqrt(3) / 6) * v - 0.5 * w
s_a = Segment(S_a, A_4)
s_b = Segment(S_a, A_3)
s_c = Segment(S_a, S_e)
s_e = Segment(S_b, A_8)
s_f = Segment(S_b, A_7)
s_g = Segment(S_f, S_e)
s_h = Segment(S_f, S_c)
s_i = Segment(A_1, S_c)
s_j = Segment(A_2, S_c)
s_d = Segment(S_b, S_e)
s_l = Segment(S_f, S_d)
s_k = Segment(A_5, S_d)
s_m = Segment(A_6, S_d)
e_1, e_2 = SDLine(A_1, A_5, A_4, A_2)
e_3, e_4 = SDLine(A_2, A_6, A_1, A_3)
e_e, e_f = SDLine(A_3, A_7, A_2, A_4)
e_g, e_h = SDLine(A_4, A_8, A_3, A_1)
e_i, e_j = SDLine(A_3, A_4, A_7, A_2)
e_k, e_l = SDLine(A_1, A_4, A_2, A_5)
e_m, e_n = SDLine(A_2, A_1, A_3, A_6)
e_o, e_p = SDLine(A_3, A_2, A_4, A_7)
e_q, e_r = SDLine(A_5, A_8, A_1, A_6)
e_s, e_t = SDLine(A_5, A_6, A_8, A_1)
e_u, e_v = SDLine(A_7, A_6, A_3, A_8)
e_w, e_x = SDLine(A_8, A_7, A_4, A_5)
a_a, a_b = SDLine(D_1, A_1, A_4, A_2)
a_c, a_d = SDLine(D_2, D_1, A_3, A_2)
a_e, a_f = SDLine(D_2, A_2, A_1, A_3)
a_g, a_h = SDLine(D_1, A_4, A_3, A_1)
a_i, a_j = SDLine(D_2, A_3, A_2, A_4)
a_k, a_l = SDLine(A_1, C_1, B_1, A_2)
a_m, a_p = SDLine(A_2, C_1, A_1, B_2)
a_o, a_t = SDLine(A_2, B_2, C_1, B_3)
a_q, a_r = SDLine(A_3, B_3, B_2, B_4)
a_y, a_z = SDLine(B_2, B_3, D_3, D_2)
a_0, a_1 = SDLine(A_1, B_1, A_4, C_1)
a_{39}, a_2 = SDLine(A_4, B_4, C_2, A_1)
a_u, a_v = SDLine(B_4, B_1, D_4, D_1)
a_n, a_w = SDLine(A_3, C_2, B_3, A_4)
a_x, a_s = SDLine(A_4, C_2, A_3, B_4)
a_3, a_4 = SDLine(C_2, C_3, B_3, B_4)
a_5, a_{22} = SDLine(C_3, A_7, B_3, D_3)
a_8, a_9 = SDLine(B_4, A_8, C_2, A_5)
a_{10}, a_{13} = SDLine(B_1, A_5, D_4, C_4)
a_{11}, a_{12} = SDLine(C_1, C_4, B_1, B_2)
a_{14}, a_{21} = SDLine(C_4, A_5, A_1, A_6)
a_{19}, a_{20} = SDLine(C_4, A_6, A_5, A_2)
a_{17}, a_{18} = SDLine(B_2, A_6, A_2, A_7)
a_{15}, a_{16} = SDLine(B_3, A_7, D_3, C_3)
a_{23}, a_{24} = SDLine(D_3, A_7, A_8, A_6)
a_{25}, a_{26} = SDLine(D_4, D_3, A_8, A_5)
a_{27}, a_{28} = SDLine(D_3, A_6, A_7, A_5)
a_{29}, a_{30} = SDLine(D_4, A_8, A_5, A_7)
a_{31}, a_{32} = SDLine(D_4, A_5, A_6, A_8)
a_{37}, a_{38} = SDLine(C_3, A_8, D_3, A_4)
Rec_1, b_5, b_6, b_7, b_8 = Polygon(B_1, B_2, B_3, B_4)
Rec_2, c_5, c_6, c_7, c_8 = Polygon(C_1, C_2, C_3, C_4)
Rec_3, d_5, d_6, d_7, d_8 = Polygon(D_1, D_4, D_3, D_2)
n = 0 (slider from 0 to 28, step 1)
poly2 = Poly_B5(D_1, D_2, A_3, C_2, A_4)
poly3 = Poly_B5(A_4, C_2, C_3, A_8, B_4)
poly1 = Poly_B5(D_1, A_4, B_4, B_1, A_1)
poly4 = Poly_B5(B_1, B_4, A_8, D_4, A_5)
poly5 = Poly_B5(A_3, B_3, A_7, C_3, C_2)
poly6 = Poly_B5(A_8, C_3, A_7, D_3, D_4)
poly7 = Poly_B5(A_2, C_1, C_4, A_6, B_2)
poly8 = Poly_B5(D_2, D_1, A_1, C_1, A_2)
poly9 = Poly_B5(D_2, A_2, B_2, B_3, A_3)
poly10 = Poly_B5(C_4, A_5, D_4, D_3, A_6)
poly11 = Poly_B5(A_1, B_1, A_5, C_4, C_1)
poly12 = Poly_B5(B_3, B_2, A_6, D_3, A_7)
poly13 = Poly_R4(A_4, A_1, A_2, A_3)
poly14 = Poly_R4(A_1, A_5, A_6, A_2)
poly15 = Poly_R4(A_1, A_4, A_8, A_5)
poly16 = Poly_R4(A_3, A_2, A_6, A_7)
poly17 = Poly_R4(A_4, A_3, A_7, A_8)
poly18 = Poly_R4(A_7, A_6, A_5, A_8)
M_1: O + (1 + sqrt(5)) / 4 * u + 1 / 2 * v + (3 + sqrt(5)) / 4 * w
θ = 4.845034003536259 rad (slider from 0 to 6.283185307179586, step 0.1*°)
S_1: M_1 + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * u + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w
poly_a, d_1, s_1, a_6 = Polygon(S_1, A_1, D_1)
k_1 = Segment(S_1, D_1)
k_{SM} = Segment(S_1, M_1)
M_2 = Midpoint(A_3, D_2)
S_2: M_2 - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * u - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w
k_{MS} = Segment(M_2, S_2)
poly_b, d_2, s_2, a_7 = Polygon(S_2, A_3, D_2)
k_2 = Segment(S_2, A_3)
k_3 = Segment(S_2, D_2)
c_c = CurveCartesian(x(M_1 + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * u + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), y(M_1 + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * u + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), θ, 0, 6.28319)
c_d = CurveCartesian(x(M_2 - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * u - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), y(M_2 - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * u - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), θ, 0, 6.28319)
M_4: (D_4 + A_5) / 2
M_3: (D_3 + A_7) / 2
M_5: (C_1 + A_1) / 2
M_6: (C_4 + A_6) / 2
S_3: M_3 - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * u - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w
c_e = CurveCartesian(x(M_3 - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * u - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), y(M_3 - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * u - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), θ, 0, 6.283185307179586)
S_4: M_4 + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) - sqrt(3) / 6 * sin(θ)) * u + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w
c_f = CurveCartesian(x(M_4 + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) - sqrt(3) / 6 * sin(θ)) * u + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), y(M_4 + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) - sqrt(3) / 6 * sin(θ)) * u + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), θ, 0, 6.283185307179586)
S_5: M_5 + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w
c_g = CurveCartesian(x(M_5 + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w), y(M_5 + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w), θ, 0, 6.283185307179586)
S_6: M_6 - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w
c_h = CurveCartesian(x(M_6 - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w), y(M_6 - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w), θ, 0, 6.283185307179586)
M_7: (A_7 + C_3) / 2
M_8: (A_4 + C_2) / 2
S_8: M_8 + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w
S_7: M_7 - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w
c_i = CurveCartesian(x(M_7 - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w), y(M_7 - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w), θ, 0, 6.283185307179586)
c_j = CurveCartesian(x(M_8 + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w), y(M_8 + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * v + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * w), θ, 0, 6.283185307179586)
M_9: (A_1 + B_1) / 2
M_{10}: (B_4 + A_8) / 2
S_9: M_9 + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w
S_{10}: M_{10} + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w
c_k = CurveCartesian(x(M_9 + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), y(M_9 + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), θ, 0, 6.283185307179586)
c_l = CurveCartesian(x(M_{10} + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), y(M_{10} + (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), θ, 0, 6.283185307179586)
M_{11}: (B_3 + A_7) / 2
M_{12}: (A_2 + B_2) / 2
S_{11}: M_{11} - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w
S_{12}: M_{12} - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w
c_m = CurveCartesian(x(M_{11} - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), y(M_{11} - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u - ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v - ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), θ, 0, 6.283185307179586)
c_n = CurveCartesian(x(M_{12} - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), y(M_{12} - (sqrt(3) / 6 * cos(θ) - (3 * sqrt(3) - sqrt(15)) / 12 * sin(θ)) * u + ((sqrt(15) - sqrt(3)) / 12 * cos(θ) + sqrt(3) / 6 * sin(θ)) * v + ((3 * sqrt(3) - sqrt(15)) / 12 * cos(θ) + (sqrt(3) - sqrt(15)) / 12 * sin(θ)) * w), θ, 0, 6.283185307179586)
Rec1, b_1, b_2, b_3, b_4 = Polygon(B_1, B_2, B_3, B_4)
Rec2, c_1, c_2, c_3, c_4 = Polygon(C_1, C_2, C_3, C_4)
Rec3, d_3, d_4, d_9, d_{10} = Polygon(D_1, D_2, D_3, D_4)
w0 = 1.2612118989768049
S1: O + w0 * u
S2: O - w0 * u
f_1 = Segment(S1, B_1)
f_2 = Segment(S1, B_4)
f_3 = Segment(S2, B_2)
f_4 = Segment(S2, B_3)
f_0 = Segment(S2, S1)
S3: O + w0 * v
S4: O - w0 * v
g_1 = Segment(S3, C_1)
g_2 = Segment(S3, C_4)
g_3 = Segment(S4, C_2)
g_4 = Segment(S4, C_3)
g_0 = Segment(S4, S3)
S5: O + w0 * w
S6: O - w0 * w
h_1 = Segment(S5, D_1)
h_2 = Segment(S5, D_2)
h_3 = Segment(S6, D_3)
h_4 = Segment(S6, D_4)
h_0 = Segment(S6, S5)
poly19 = Poly_P3(S5, S1, S3)
poly20 = Poly_P3(S3, S1, S6)
poly21 = Poly_P3(S5, S3, S2)
poly22 = Poly_P3(S2, S3, S6)
poly23 = Poly_P3(S5, S2, S4)
poly24 = Poly_P3(S4, S2, S6)
poly25 = Poly_P3(S5, S4, S1)
poly26 = Poly_P3(S1, S4, S6)
SS_b: O - k_0 * u - k_0 * v
SS_c: O + k_0 * v + k_0 * w
SS_d: O - k_0 * v - k_0 * w
SS_e: O - (sqrt(2) - 3 * sqrt(5) + 2 * sqrt(15)) / 36 * u - (-2 * sqrt(2) - sqrt(5) - 3) / 36 * v - (sqrt(2) + sqrt(30) - sqrt(10) + sqrt(6)) / 24 * w
SS_f: O - (-2 * sqrt(2) - sqrt(5) - 3) / 36 * u - (sqrt(2) - 3 * sqrt(5) + 2 * sqrt(15)) / 36 * v - (sqrt(2) + sqrt(30) - sqrt(10) + sqrt(6)) / 24 * w
i_3 = Segment(S4, SS_b)
SS_a: O + k_0 * u + k_0 * v
i_7 = Segment(SS_a, SS_c)
i_9 = Segment(SS_f, SS_e)
i_a = Segment(SS_f, SS_b)
i_b = Segment(SS_d, SS_b)
j_0 = Segment(A_1, S5)
j_1 = Segment(A_1, D_1)
j_2 = Segment(A_3, D_2)
j_4 = Segment(A_8, D_4)
j_3 = Segment(A_6, D_3)
j_5 = Segment(B_3, A_7)
j_6 = Segment(B_2, A_2)
j_7 = Segment(B_4, A_4)
j_8 = Segment(B_1, A_5)
i_1 = Segment(S5, SS_c)
i_6 = Segment(S2, SS_b)
i_5 = Segment(S1, SS_a)
i_2 = Segment(S6, SS_d)
i_8 = Segment(SS_a, SS_d)
m_1 = Segment(A_1, D_1)
m_2 = Segment(A_3, D_2)
m_4 = Segment(A_8, D_4)
m_3 = Segment(A_6, D_3)
m_5 = Segment(A_2, C_1)
m_6 = Segment(A_5, C_4)
m_7 = Segment(A_4, C_2)
m_8 = Segment(A_7, C_3)
m_9 = Segment(A_5, B_1)
m_{11} = Segment(A_7, B_3)
m_{10} = Segment(A_6, B_2)
m_{12} = Segment(A_8, B_4)
t = 1.261 (slider from 0 to 1.618033988749895, step 0.0010)
k_5: (1 - (2 + sqrt(3)) / sqrt(29 - 4 * sqrt(3))) * t
S_α: O + k_5 * u + k_5 * v
S_β: O - k_5 * u - k_5 * v
S_γ: O + k_5 * v + k_5 * w
S_δ: O - k_5 * v - k_5 * w
SS1: O + t * u
SS2: O - t * u
SS3: O + t * v
SS4: O - t * v
SS5: O + t * w
SS6: O - t * w
n_1 = Segment(S_α, S_γ)
n_2 = Segment(S_α, S_δ)
n_3 = Segment(S_β, S_δ)
n_4 = Segment(S_γ, SS5)
n_5 = Segment(S_α, SS1)
n_7 = Segment(S_δ, SS6)
n_8 = Segment(S_β, SS2)
n_9 = Segment(S_β, SS4)
n_a = Segment(D_1, SS5)
n_b = Segment(D_2, SS5)
n_c = Segment(D_3, SS6)
n_d = Segment(D_4, SS6)
n_e = Segment(C_1, SS3)
n_f = Segment(C_4, SS3)
n_g = Segment(C_2, SS4)
n_h = Segment(C_3, SS4)
n_i = Segment(B_1, SS1)
n_j = Segment(B_4, SS1)
n_k = Segment(B_2, SS2)
n_l = Segment(B_3, SS2)
inputBox1 = Textfield(t)
y_O = false
E_1 = Midpoint(j_7)
E_2 = Midpoint(j_4)
E_3 = Midpoint(j_8)
E_4 = Midpoint(j_3)
E_5 = Midpoint(j_1)
E_6 = Midpoint(j_2)
E_7 = Midpoint(j_6)
E_8 = Midpoint(j_5)
a = false
text28: "$目前路徑長為$
$" + (LaTeX[(2 + sqrt(3) + sqrt(29 - 4 * sqrt(3))) / sqrt(2) * t]) + "+12×" + (LaTeX[sqrt(t^(2) - (sqrt(5) + 1) * t + 3)]) + "+8(\sqrt5-1)$
$=" + (LaTeX[(2 + sqrt(3) + sqrt(29 - 4 * sqrt(3))) / sqrt(2) * t]) + "+" + (LaTeX[12 * sqrt(t^(2) - (sqrt(5) + 1) * t + 3)]) + "+9.889$
$=" + (LaTeX[If[a ≟ true, (2 + sqrt(3) + sqrt(29 - 4 * sqrt(3))) / sqrt(2) * t + 12 * sqrt(t^(2) - (sqrt(5) + 1) * t + 3) + 9.889]]) + "" + (LaTeX[If[a ≠ true, round(1000 * ((2 + sqrt(3) + sqrt(29 - 4 * sqrt(3))) / sqrt(2) * t + 12 * sqrt(t^(2) - (sqrt(5) + 1) * t + 3) + 9.889)) / 1000]]) + "$"
i_4 = Segment(S3, SS_c)
n_6 = Segment(S_γ, SS3)

Tool: SDLine
Input: A, B, C, D
Output: g, h

b: sgn(sin(Angle[D, B, A]))
a: sgn(sin(Angle[A, B, C]))
c: sgn(a + b + 0.5)
d: sqrt(c)
e: sqrt(-c)
E = Midpoint(A, B)
A' = Dilate(A, d, E)
B' = Dilate(B, d, E)
g = Segment(A', B')
A'_1 = Dilate(A, e, E)
B'_1 = Dilate(B, e, E)
h = Segment(A'_1, B'_1)

Tool: Poly_B5
Input: A, B, C, D, E
Output: poly1'

poly1, a, b, c, d, e = Polygon(A, B, C, D, E)
F = Midpoint(b)
G = Midpoint(d)
α = Angle(G, F, A)
f: sqrt(sgn(sin(α)))
A' = Dilate(A, f, A)
B' = Dilate(B, f, A)
C' = Dilate(C, f, A)
D' = Dilate(D, f, A)
E' = Dilate(E, f, A)
poly1', a', b', c', d', e' = Polygon(A', B', C', D', E')

Tool: Poly_R4
Input: A, B, C, D
Output: poly1'

α = Angle(C, B, A)
a: sqrt(sgn(sin(α)))
A' = Dilate(A, a, B)
B' = Dilate(B, a, B)
C' = Dilate(C, a, B)
D' = Dilate(D, a, B)
poly1', a', b', c', d' = Polygon(A', B', C', D')

Tool: Poly_P4
Input: A, B, C, D
Output: poly1

poly1 = Poly_R4(A, B, C, D)

Tool: Poly_B3
Input: A, B, C
Output: poly1'

α = Angle(C, B, A)
d: sqrt(sgn(sin(α)))
A' = Dilate(A, d, A)
B' = Dilate(B, d, A)
C' = Dilate(C, d, A)
poly1', c', a', b' = Polygon(A', B', C')

Tool: Poly_P3
Input: A, B, C
Output: poly1

poly1 = Poly_B3(A, B, C)