兩面角的平面角
Author: 藍邦偉 老師

x

y

z

單位向量

座標軸

兩面角的平面角

θ

顯示正確角度

θ

如何定義兩面角?

180°-θ

Reset

O = (8.29784216522883, 3.395594392080685)
β = 1.2566370614359172 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 4.276056667386108 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
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})
A_b: O - 4 * u
A_a: O + 4 * u
B = Midpoint(A_a, A_b)
θ = 0.9599310885968813 rad (slider from 0 to 3.141592653589793, step 0.008726646259971648)
A_e: O + 4 * u + 3 * cos(θ) * v + 4 * sin(θ) * w
A_f: O - 4 * u + 3 * cos(θ) * v + 4 * sin(θ) * w
A = Midpoint(A_e, A_f)
A' = Mirror(A, B)
G = Mirror(A_f, A_b)
F = Mirror(A_e, A_a)
A_d: O + 4 * u + 3 * v
A_c: O - 4 * u + 3 * v
K = Mirror(A_c, A_b)
J = Mirror(A_d, A_a)
L = 6 (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)
A_1: O + L * u
B_1: O + L * v
Z: O + L * w
c = false
多邊形1, l, m, n, p = Polygon(K, J, A_d, A_c)
多邊形2, q, s_1, t, a_1 = Polygon(A_e, F, G, A_f)
d = false
C = Midpoint(A_d, A_c)
f = Segment(B, C)
θ_1 = Angle(C, B, A)
r = 0.19 (slider from 0 to 1, step 0.01)
u_1 = Vector(A_e, A_f)
D: A_e + (0.1 * Random[0, 10] + r * 0) * u_1
E: A_d + (0.1 * Random[0, 10] + r * 0) * u_1
g = false
ε = Angle(D, B, E)
j = false
b_1 = Segment(A_a, A_b)
e = Segment(A, A')
c_1 = Circle(B, 0.3)
M = Intersect(c_1, b_1, 1)
N = Intersect(c_1, e, 1)
P = Intersect(c_1, f, 1)
H: N + M - B
I: M + P - B
k = Segment(N, H)
d_1 = Segment(M, H)
e_1 = Segment(M, I)
f_1 = Segment(P, I)
Q = (14.935877626947564, 7.904531667270681)
g_1 = Circle(Q, 1)
P_1: Q + (1, 0)
R = Rotate(P_1, θ, Q)
h_1 = Segment(Q, P_1)
i_1 = Segment(Q, R)
γ = Angle(P_1, Q, R)
C' = Mirror(C, B)
s = 1 (slider from 1 to 3, step 1)
j_1 = Segment(C', B)
k_1 = Segment(B, A')
h = Vector(B, D)
i = Vector(B, E)
v_1 = Vector(B, A)
w_1 = Vector(B, C)
z_1 = Vector(B, C')
δ = Angle(A, B, C')
l_1 = Segment(C, C')
文字2: "目前角度" + (LaTeX[θ]) + ""
文字3: "與" + (LaTeX[180° - θ]) + ""