共頂點且夾角為30度的三條射線
Author: 藍邦偉　老師

單位向量

座標軸

x

y

z

顯示輔助平面

夾角相同且共頂

點的三條射線

顯示三角形

O

P

Q

R

S

顯示相關數據

$ \overline{OP}=\overline{OR}=1 $

$ \overline{OS}=\frac{\sqrt{3}}{2} $

$ \overline{PR}=\frac{\sqrt{6}-\sqrt{2}}{2} $

\overline{RS}=\overline{PS}=\frac{1}{2}

$ \overline{PQ}=\sqrt{3\sqrt{3}-5} $

$ \overline{OQ}=\frac{3\sqrt{2}-\sqrt{6}}{2} $

α = 3.9269908169872414 rad (slider from 0 to 6.283185307179586, step 0.01*°)
β = 1.1344640137963142 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
O = (6.9954989275337045, 1.3767109799682562)
X_{unit}: O + (cos(α), sin(α) * cos(β))
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
Z_{unit}: O + (0, sin(β))
u = Vector(O, X_{unit})
v = Vector(O, Y_{unit})
w = Vector(O, Z_{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: 0.2 * Corner[2] + 0.8 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
多邊形1, e, q_2, q_3, f = Polygon(Corner[1], Q_2, Q_3, Corner[4])
g = Segment(Q_2, Q_3)
S: O + sqrt(3) * sin(15°) * u + sqrt(3) * cos(15°) * v
R: O - 2 * sin(15°) * u + 2 * cos(15°) * v
h_4 = Ray(O, S)
h_5 = Ray(O, R)
P: O + (3 * sqrt(2) - sqrt(6)) * v + 2 * sqrt(3 * sqrt(3) - 5) * w
h_3 = Ray(O, P)
Q: O + (3 * sqrt(2) - sqrt(6)) * v
h_1 = Segment(P, Q)
A'' = Mirror(R, O)
A' = Mirror(S, O)
E_1, i, j, k, l = Polygon(S + 2 * u + 2 * v, R - 2 * u + 2 * v, A' - 2 * u - 2 * v, A'' + 2 * u - 2 * v)
A = Mirror(P, O)
m = false
h_2 = Segment(S, R)
Tri1 = Poly_B3(P, O, S)
Tri2 = Poly_B3(P, R, O)
Tri3 = Poly_B3(S, O, R)
h_a = Segment(R, P)
h_b = Segment(S, P)
h = false
n = false
o = false

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_Y3
Input: A, B, C
Output: poly1

poly1 = Poly_B3(A, B, C)

Tool: Poly_B3 (command Poly_B31)
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_C3
Input: A, B, C
Output: poly1

poly1 = Poly_B3(A, B, C)

Tool: Poly_R3
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')