Beweis der Benfordverteilung
Author: Prof. Dr. Dörte Haftendorn
Date: 12 Mai 2013

lg(x)

lg(10x)

lg(100x)

grüne Werte: Startziffer 2

braune Werte: Startziffer 1

lg(1000x)

blaue Werte: Startziffer 3 (Teil)

Ha 07

f(x) = lg(x)
g(x) = lg(x) + 1
h(x) = lg(x) + 2
f1(x) = lg(x) + 3
A = Intersect(f1, i, (2, 3.3010299956639813))
B = Intersect(h, i, (2, 2.3010299956639813))
C = Intersect(g, i, (2, 1.3010299956639813))
D = Intersect(f, i, (2, 0.30102999566398114))
l = OrthogonalLine(A, yAxis)
m = OrthogonalLine(B, yAxis)
n = OrthogonalLine(C, yAxis)
p = OrthogonalLine(D, yAxis)
poly1, q, r, s, t, a1, b1, c1 = Polygon((10, 0), (20, 0), (20, y(C)), (0, y(C)), (0, 1), (10, 1), (10, 0))
poly2, d1, e1, g1, h1, i1, j1, k1 = Polygon((100, 0), (200, 0), (200, y(B)), (0, y(B)), (0, 2), (100, 2), (100, 0))
poly3, l1, m1, n1, p1, q1, r1, s1 = Polygon((1000, 0), (2000, 0), (2000, y(A)), (0, y(A)), (0, 3), (1000, 3), (1000, 0))
poly4, t1, a2, d_1, b2, c2, d2, e2 = Polygon((1, 0), (2, 0), D, (0, y(D)), (0, 0), (1, 0), (1, 0))
Lg1000 = Intersect(yAxis, c)
Lg100 = Intersect(yAxis, b)
Lg10 = Intersect(yAxis, a)
Lg10000 = Intersect(yAxis, d)
E = Intersect(f1, j, (3, 3.4771212547196626))
F = Intersect(h, j, (3, 2.4771212547196626))
G = Intersect(g, j, (3, 1.4771212547196624))
H = Intersect(f, j, (3, 0.47712125471966244))
poly5, f2, g2, h2, i2, j2, k2, l2 = Polygon((2, 0), (3, 0), H, (0, y(H)), (0, y(D)), D, (2, 0))
poly6, m2, n2, p2, q2, r2, s2, t2 = Polygon((20, 0), (30, 0), (30, y(G)), (0, y(G)), (0, y(C)), (20, y(C)), (20, 0))
poly7, a3, b3, c3, d3, e3, f3, g3 = Polygon((200, 0), (300, 0), (300, y(F)), (0, y(F)), (0, y(B)), (200, y(B)), (200, 0))
poly8, h3, i3, j3, k3, l3, m3, n3 = Polygon((2000, 0), (3000, 0), (3000, y(E)), (0, y(E)), (0, y(A)), (2000, y(A)), (2000, 0))
I = Intersect(f, k, (4, 0.6020599913279623))
poly9, p3, q3, r3, s3, t3, a4, b4 = Polygon((3, 0), (4, 0), (4, y(I)), (0, y(I)), (0, y(H)), (3, y(H)), (3, 0))