Fixed Point Problem
Author: 藍邦偉老師

$ A $

$ B $

$ C $

D

$ Fixed\; Point \;Problem $

r_1 = 0.7 (slider from 0 to 1, step 0.01)
r_2 = 0.7 (slider from 0 to 1, step 0.01)
r_3 = 0.7 (slider from 0 to 1, step 0.01)
r_4 = 0.7 (slider from 0 to 1, step 0.01)
k = 4 (slider from 1 to n, step 1)
n = 24 (slider from 1 to 50, step 1)
A = (1.52, -2.84)
a_a = Ray(A, A + (1, 0))
B = Point(a_a)
poly1, a, b, c, d, C, D = Polygon(A, B, 4)
P_1 = Dilate(B, r_1, A)
E = Midpoint(A, C)
α_1 = Angle(A, E, P_1)
P_3 = Dilate(C, r_3, D)
P_2 = Dilate(C, r_2, B)
P_4 = Dilate(A, r_4, D)
α_2 = Angle(B, E, P_2)
α_3 = Angle(C, E, P_3)
α_4 = Angle(D, E, P_4)
q_1: Segment[E, P_1] / Segment[E, A]
q_2: Segment[E, P_2] / Segment[E, B]
q_3: Segment[E, P_3] / Segment[E, C]
q_4: Segment[E, P_4] / Segment[E, D]
list_1 = Sequence(Rotate[Dilate[A, q_1^(k - 1), E], (k - 1) * α_1, E], k, 1, n)
list_2 = Sequence(Rotate[Dilate[B, q_2^(k - 1), E], (k - 1) * α_1, E], k, 1, n)
list_3 = Sequence(Rotate[Dilate[C, q_3^(k - 1), E], (k - 1) * α_1, E], k, 1, n)
list_4 = Sequence(Rotate[Dilate[D, q_4^(k - 1), E], (k - 1) * α_1, E], k, 1, n)
poly2, e, f, g, h = Polygon(Element[list_1, Min[k, n]], Element[list_2, Min[k, n]], Element[list_3, Min[k, n]], Element[list_4, Min[k, n]])
List = Sequence(Polygon[Element[list_1, k], Element[list_2, k], Element[list_3, k], Element[list_4, k]], k, 1, n)