Goldene Spirale mit Polarkoordinaten, Längeneigenschaften
Author: Prof.  Dr. Dörte Haftendorn

Die Aussagen befinden sich in der pdf-Datei.

Ha 2/11

Phi = 1.618033988749895
A = (-5, 4)
B = (10.5, 4)
a = Line(A, B)
Theta = Point(a)
θ: x(Theta)
li = Sequence((Phi^(2.0 / 3.141592653589793 * (θ + 2.0 * 3.141592653589793 / 40.0 * i)) * cos(θ + 2.0 * 3.141592653589793 / 40.0 * i), Phi^(2.0 / 3.141592653589793 * (θ + 2.0 * 3.141592653589793 / 40.0 * i)) * sin(θ + 2.0 * 3.141592653589793 / 40.0 * i)), i, 1.0, 30.0)
r: Phi^(2.0 / 3.141592653589793 * θ)
px: r * cos(θ)
py: r * sin(θ)
P_0: (px, py)
Ortslinie1 = Locus(P_0, Theta)
O = (0, 0)
b = Segment(O, P_0)
P_2 = Element(li, 20.0)
c = Segment(O, P_2)
d = OrthogonalLine(P_0, b)
e = OrthogonalLine(P_2, c)
C = Intersect(d, e)
Vieleck1, o, p, c_1, ps = Polygon(O, P_0, C, P_2)
f = AngularBisector(P_0, O, P_2)
xpm: Phi^(2.0 / 3.141592653589793 * (θ + 2.0 * 3.141592653589793 / 4.0)) * cos(θ + 2.0 * 3.141592653589793 / 4.0)
ypm: Phi^(2.0 / 3.141592653589793 * (θ + 2.0 * 3.141592653589793 / 4.0)) * sin(θ + 2.0 * 3.141592653589793 / 4.0)
P_1: (xpm, ypm)
g = Segment(O, P_1)
Vieleck2, r_0, p_1, h, i, j, k, b_0, m, n, q, s, t = Polygon(O, P_0, Element[li, 1.0], Element[li, 2.0], Element[li, 3.0], Element[li, 4.0], Element[li, 5.0], Element[li, 6.0], Element[li, 7.0], Element[li, 8.0], Element[li, 9.0], Element[li, 10.0])
Vieleck3, r_1, b_3, d_1, e_1, f_1, g_1, b_1, i_1, j_1, k_1, l_1, r_2 = Polygon(O, P_1, Element[li, 11.0], Element[li, 12.0], Element[li, 13.0], Element[li, 14.0], Element[li, 15.0], Element[li, 16.0], Element[li, 17.0], Element[li, 18.0], Element[li, 19.0], Element[li, 20.0])
Vieleck4, o_2, p_s, n_1, q_1, r_4, s_1, b_2, a_2, b_5, c_2, d_2, r_3 = Polygon(O, P_2, Element[li, 21.0], Element[li, 22.0], Element[li, 23.0], Element[li, 24.0], Element[li, 25.0], Element[li, 26.0], Element[li, 27.0], Element[li, 28.0], Element[li, 29.0], Element[li, 30.0])
P_3 = Element(li, 30.0)