Spiralen in Dreiecken
Author: Prof. Dr. Dieter Riebesehl
Date: März 2011

Interessant ist k = 0.754878

Eigenschaften
der
Spirale

Zu bewegen:
A bestimmt die Lage
B bestimmt die Größe
D bestimmt den Streckfaktor

A = (-4.0200000000000005, 4.62)
B = (4.451581843191197, -4.058156808803301)
Vieleck1, a, a_1, b, C = Polygon(A, B, 3.0)
D = Point(a_1)
Vieleck2, c, c_1, d, E = Polygon(C, D, 3.0)
e = Segment(C, B)
f = Segment(C, D)
k: f / e
D' = Dilate(D, k, E)
Vieleck3, g, e_1, d', F = Polygon(E, D', 3.0)
h = Segment(A, F)
i = Segment(E, B)
G = Intersect(h, i)
D'' = Dilate(D', k, F)
Vieleck4, j, f_1, d'', H = Polygon(F, D'', 3.0)
I = Intersect(h, f_1)
Vieleck5, l, h_1, i_1, J = Polygon(H, I, 3.0)
m = Segment(D', H)
K = Intersect(h_1, m)
Vieleck6, n, j_1, k_1, L = Polygon(J, K, 3.0)
M = Intersect(j_1, i)
Vieleck7, p, l_1, m_1, N = Polygon(L, M, 3.0)
q = CircleArc(B, C, A)
r = CircleArc(D, E, C)
t = CircleArc(D'', H, F)
d_1 = CircleArc(I, J, H)
g_1 = CircleArc(K, L, J)
p_1 = CircleArc(M, N, L)
s = 5.54 (slider from -5 to 10, step 0.01)
min = -13 (slider from -13 to 5, step 0.1)
max = 2.7 (slider from -5 to 7, step 0.1)
o = CurveCartesian(x(G) + s * k^(-3.0 * α / 3.141592653589793) * cos(α), y(G) + s * k^(-3.0 * α / 3.141592653589793) * sin(α), α, min, max)
q_1 = CircleArc(D', F, E)
Text1: "Schrupffaktor k = " + k