微分的應用(2)
Author: 藍邦偉　老師

$O$

單位向量

座標軸

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微分的應用(2)

R = 4 (slider from 1 to 5, step 0.1)
h = 1.6 (slider from 0.1 to 2 * R - 0.2, step 0.1)
O = (9.983198507335322, 3.2486778547375113)
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 = 7 (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]))
g = Segment(Q_2, Q_3)
poly1, h_1, q_1, q_4, i = Polygon(Corner[1], Q_2, Q_3, Corner[4])
r: sqrt(R^(2) - (h - R)^(2))
c_1 = CurveCartesian(x(O + r * cos(t) * u + r * sin(t) * v + (h - R) * w), y(O + r * cos(t) * u + r * sin(t) * v + (h - R) * w), t, 0, 6.28319)
A_a = Point(c_1)
A_b = Point(c_1)
A_c = Point(c_1)
A_d = Point(c_1)
A_e = Point(c_1)
c_2 = Conic(A_a, A_b, A_c, A_d, A_e)
O_1: O
A_1: O_1 + R * w
l_1, l_2 = Tangent(A_1, c_2)
A_E = Intersect(c_2, l_1)
A_F = Intersect(c_2, l_2)
e = Segment(A_1, A_E)
f = Segment(A_1, A_F)
C_3 = Circle(O_1, R)
j = Segment(A_1, O_1 + (h - R) * w)
K_1: O_1 + (h - R) * w
l_3: y = y(K_1)
A_H, A_G = Intersect(c_2, l_3)
c_3 = CurveCartesian(x(O + R * cos(t) * u + R * sin(t) * v), y(O + R * cos(t) * u + R * sin(t) * v), t, 0, 6.283185307179586)
n = 2 (slider from 2 to 50, step 1)
list1 = Sequence(Segment[A_1, O + sqrt(R^(2) - (h - R)^(2)) * cos(i * 2 * π / n) * u + sqrt(R^(2) - (h - R)^(2)) * sin(i * 2 * π / n) * v + (h - R) * w], i, 1, n)