微分的應用(6)
Author: 藍邦偉　老師

單位向量

座標軸

x

y

z

微分的應用(6)

輔助線

O = (7.8652907909478955, 3.2769570841304927)
β = 1.3962634015954636 rad (slider from 0 to 6.283185307179586, step 0.1*°)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 4.276056667386108 rad (slider from 0 to 6.283185307179586, step 0.1*°)
X_{unit}: O + (cos(α), sin(α) * cos(β))
u = Vector(O, X_{unit})
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
v = Vector(O, Y_{unit})
L = 3 (slider from 1 to 10, step 1)
a = Vector(O - L * v, O + L * v)
b = Vector(O - L * w, O + L * w)
z = Vector(O - L * u, O + L * u)
c = false
d = false
Q_2: 0.5 * Corner[2] + 0.5 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
g = Segment(Q_2, Q_3)
Base, h, q_1, q_4, i = Polygon(Corner[1], Q_2, Q_3, Corner[4])
x_1 = 1 (slider from 0.1 to 5, step 0.1)
x_2 = 2 (slider from 0.1 to 5, step 0.1)
x_3 = 1 (slider from 0.1 to 5, step 0.1)
y_1 = 1 (slider from 0.1 to 5, step 0.1)
y_2 = 1 (slider from 0.1 to 5, step 0.1)
y_3 = 1 (slider from 0.1 to 5, step 0.1)
z_1 = 1 (slider from 0.1 to 5, step 0.1)
z_2 = 2 (slider from 0.1 to 5, step 0.1)
A = (12.146819415083218, 4.00453711176133)
A_A: A + (2, 0)
A_B: A + (1, sqrt(3))
A_C: A_B - (2, 0)
A_D: A - (2, 0)
A_E: A - (1, sqrt(3))
A_F: A_E + (2, 0)
a_1 = Segment(A_A, A_B)
a_2 = Segment(A_C, A_B)
a_3 = Segment(A_C, A_D)
a_4 = Segment(A_E, A_D)
a_5 = Segment(A_E, A_F)
n = 0.7 (slider from 0.1 to 1.6, step 0.1)
m: n / sqrt(3)
a_6 = Segment(A_A, A_F)
B_1: A_B + (-m, -n)
B_2: A_B - (m, 0)
e = OrthogonalLine(B_1, a_1)
B_3 = Intersect(e, a_1)
C_1 = Mirror(B_1, A)
C_2 = Mirror(B_2, A)
C_3 = Mirror(B_3, A)
B_4: A_C + (m, -n)
B_5: A_C + (m, 0)
f = OrthogonalLine(B_4, a_3)
B_6 = Intersect(a_3, f)
C_4 = Mirror(B_4, A)
C_5 = Mirror(B_5, A)
C_6 = Mirror(B_6, A)
B_7 = Rotate(B_4, 1.0471975511965976, A)
C_7 = Rotate(C_4, 1.0471975511965976, A)
j = OrthogonalLine(B_7, a_3)
k: 2 - 2 * m
B_8 = Intersect(a_3, j)
B_9 = Intersect(e, a_4)
C_8 = Mirror(B_8, A)
C_9 = Mirror(B_9, A)
b_1 = Segment(B_1, B_4)
b_2 = Segment(B_7, B_4)
b_3 = Segment(B_7, C_1)
b_4 = Segment(C_4, C_1)
b_5 = Segment(C_4, C_7)
b_6 = Segment(C_7, B_1)
Poly_a, b_7, b_8, a_b, b_9 = Polygon(B_1, B_2, A_B, B_3)
Poly_b, b_{10}, b_{11}, a_c, b_{12} = Polygon(B_4, B_6, A_C, B_5)
B = Mirror(B_1, A)
C = Mirror(B_2, A)
D = Mirror(A_B, A)
E = Mirror(B_3, A)
F = Mirror(B_4, A)
G = Mirror(B_6, A)
H = Mirror(A_C, A)
I = Mirror(B_5, A)
Poly_e, f_1, g_1, h_1, i_1 = Polygon(F, G, H, I)
J = Mirror(B_7, A)
K = Mirror(B_9, A)
M = Mirror(A_D, A)
N = Mirror(B_8, A)
c_1 = Segment(B_1, B_3)
d_2 = Segment(B_1, B_3)
d_1 = Segment(B_1, B_2)
d_{12} = Segment(B_5, B_4)
d_{11} = Segment(B_6, B_4)
d_{10} = Segment(B_7, B_8)
d_8 = Segment(C_1, C_3)
d_7 = Segment(C_1, C_2)
d_6 = Segment(C_4, C_5)
d_5 = Segment(C_4, C_6)
d_4 = Segment(C_7, C_8)
d_3 = Segment(C_7, C_9)
P = Mirror(B_1, A)
Q = Mirror(B_2, A)
R = Mirror(A_B, A)
S = Mirror(B_3, A)
e_1 = Segment(A_A, C_7)
e_2 = Segment(A_B, B_1)
e_3 = Segment(A_C, B_4)
e_4 = Segment(B_7, A_D)
e_5 = Segment(C_1, A_E)
e_6 = Segment(C_4, A_F)
l = false
E_1: O + k * u
E_2: O + k * cos(60°) * u + k * sin(60°) * v
E_3: O + k * cos(120°) * u + k * sin(120°) * v
E_4: O + k * cos(180°) * u + k * sin(180°) * v
E_5: O + k * cos(240°) * u + k * sin(240°) * v
E_6: O + k * cos(300°) * u + k * sin(300°) * v
E_7: E_1 + n * w
E_8: E_2 + n * w
E_9: E_3 + n * w
E_{10}: E_4 + n * w
E_{11}: E_5 + n * w
E_{12}: E_6 + n * w
p_a = Segment(E_1, E_2)
p_c = Segment(E_3, E_4)
p_d = Segment(E_5, E_4)
p_e = Segment(E_5, E_6)
p_f = Segment(E_1, E_6)
p_g = Segment(E_7, E_8)
p_h = Segment(E_9, E_8)
p_2 = Segment(E_3, E_2)
p_b = Segment(E_3, E_2)
p_i = Segment(E_9, E_{10})
p_j = Segment(E_{11}, E_{10})
p_k = Segment(E_{11}, E_{12})
p_l = Segment(E_7, E_{12})
p_m = Segment(E_7, E_1)
p_n = Segment(E_8, E_2)
p_o = Segment(E_9, E_3)
p_p = Segment(E_{10}, E_4)
p_q = Segment(E_{11}, E_5)
p_r = Segment(E_{12}, E_6)
Poly_{base}, e_7, e_8, e_9, e_{10}, e_{11}, e_{12} = Polygon(E_1, E_2, E_3, E_4, E_5, E_6)
Poly_c, b_{13}, b_{14}, a_d, b_{15} = Polygon(B_7, B_9, A_D, B_8)
d_9 = Segment(B_7, B_9)
Poly_d, c_2, c_3, a_e, c_4 = Polygon(C_1, C_3, A_E, C_2)
Poly_f, c_7, c_8, a_a, c_9 = Polygon(C_7, C_8, A_A, C_9)