88聯考自然組一題
Author: 藍邦偉  老師

x

y

z

顯示xy平面

顯示單位向量

顯示座標軸

A: (x((Corner[3] + 39 * Corner[4]) / 40), y((Corner[1] + 9 * Corner[4]) / 10))
B: (x((4 * Corner[3] + 16 * Corner[4]) / 20), y((Corner[1] + 9 * Corner[4]) / 10))
a = Segment(A, B)
C: (3 * A + B) / 4
D: (3 * B + A) / 4
E = Point(a)
c = Circle(C, E)
c' = Translate(c, Vector[C, D])
A' = Rotate(A, 270*°, C)
B' = Rotate(B, 270*°, C)
a' = Segment(A', B')
c'' = Rotate(c', 270*°, C)
D' = Rotate(D, 270*°, C)
E' = Rotate(Translate[E, Vector[C, D]], 90*°, D)
E'' = Rotate(E', 270*°, C)
F = Point(c'')
G = Point(c')
α = Angle(E'', D', F)
b = Segment(D', F)
d = Segment(D, G)
β = Angle(G, D, E')
I: C + (b * cos(α), b * sin(α) * sin(β))
J: C + (b * cos(α + 90°), b * sin(α + 90°) * sin(β))
K: C + (0, b * cos(β))
e = Segment(C, K)
f = Segment(C, I)
g = Segment(C, J)
O = (-0.7250437212008725, -1.4549361758892492)
I' = Translate(I, Vector[C, O])
J' = Translate(J, Vector[C, O])
K' = Translate(K, Vector[C, O])
L = 7 (slider from 1 to 10, step 1)
I'' = Dilate(I', L, O)
J'' = Dilate(J', L, O)
K'' = Dilate(K', L, O)
I''' = Dilate(I'', -1, O)
J''' = Dilate(J'', -1, O)
K''' = Dilate(K'', -1, O)
u' = Vector(I''', I'')
v' = Vector(J''', J'')
w' = Vector(K''', K'')
h = Segment(D', E'')
i = Segment(D, E')
軌跡1 = Locus(I, F)
L_{axis}: L
j = false
w = Vector(O, K')
u = Vector(O, I')
v = Vector(O, J')
k = false
list1 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), t, -L, L], s, -L, L, 1)
list2 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), s, -L, L], t, -L, L, 1)
l = true
A_1: O + 2 * sqrt(2) * u + 4 * v
A_2: O - 2 * sqrt(2) * u + 4 * v
A_3: O - 2 * sqrt(2) * u - 4 * v
A_4: O + 2 * sqrt(2) * u - 4 * v
A_5: O + 2 * sqrt(2) * u + 4 * w
A_6: O + 2 * sqrt(2) * u - 4 * w
A_7: O - 2 * sqrt(2) * u + 4 * w
A_8: O - 2 * sqrt(2) * u - 4 * w
m = Segment(A_4, A_6)
n_1 = Segment(A_6, A_1)
p = Segment(A_1, A_5)
q = Segment(A_5, A_4)
r = Segment(A_7, A_2)
s = Segment(A_2, A_8)
t = Segment(A_8, A_3)
a_1 = Segment(A_3, A_7)
b_1 = Segment(A_5, A_7)
c_1 = Segment(A_4, A_3)
d_1 = Segment(A_6, A_8)
e_1 = Segment(A_1, A_2)
多邊形1, a_2, a_3, a_4, a_5 = Polygon(A_1, A_2, A_3, A_4)
n = 1 (slider from 0 to 1, step 1)
poly1, f_1, g_1, h_1, i_1 = Polygon(Corner[1], Corner[2], Corner[3], Corner[4])