微分的應用(7)
Author: 藍邦偉　老師

單位向量

座標軸

x

y

z

$ 微分的應用(7) $

O = (10.001376041200228, 1.238242609278878)
β = 1.7453292519943295 rad (slider from 0 to 6.283185307179586, step 0.1*°)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 0.0017453292519943296 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 = 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)
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, q_1, q_4, i = Polygon(Corner[1], Q_2, Q_3, Corner[4])
c_1 = CurveCartesian(x(O + 3 * cos(t) * u + 3 * sin(t) * v), y(O + 3 * cos(t) * u + 3 * sin(t) * v), t, 0, 6.283185307179586)
H: O + 6 * w
A = Point(c_1)
B = Point(c_1)
C = Point(c_1)
D = Point(c_1)
E = Point(c_1)
c_2 = Conic(A, B, C, D, E)
e, f = Tangent(H, c_2)
F = Intersect(c_2, e)
G = Intersect(c_2, f)
j = Segment(H, F)
k = Segment(H, G)
r = 1.2 (slider from 0.1 to 3, step 0.1)
c_4 = 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)
c_3 = CurveCartesian(x(O + r * cos(t) * u + r * sin(t) * v + (6 - 2 * r) * w), y(O + r * cos(t) * u + r * sin(t) * v + (6 - 2 * r) * w), t, 0, 6.283185307179586)
l = Segment(O, H)
I = Point(c_3)
J = Point(c_3)
K = Point(c_3)
M = Point(c_3)
N = Point(c_3)
c_5 = Conic(I, J, K, M, N)
P = Intersect(c_5, j)
Q = Intersect(c_5, k)
P_1: P - (6 - 2 * r) * w
Q_1: Q - (6 - 2 * r) * w
m = Segment(P, P_1)
n_1 = Segment(Q, Q_1)
n = 14 (slider from 2 to 20, step 1)
list_1 = Sequence(O + r * cos(2 * k * π / n) * u + r * sin(2 * k * π / n) * v, k, 1, n)
list_2 = Sequence(O + r * cos(2 * k * π / n) * u + r * sin(2 * k * π / n) * v + (6 - 2 * r) * w, k, 1, n)
list_3 = Sequence(Segment[Element[list_1, k], Element[list_2, k]], k, 1, n)