Ortskurve, die die Steigung von P anzeigt.
Author: Prof. Dr. Dörte Haftendorn

Das Fahrrad ist von Prof. Dr. Dieter Riebesehl gebaut. Die blauen Punkte können beliebig umdefiniert werden. 
Vorsicht: Ziehen der blauen Punkte ist zwar möglich, aber heikel.

1

1

Ortskurve

m

Ha 2013

gerechnet

Tangente in P

A_3 = (5.044423263989802, 3.441698528048412)
A_1 = (0.4426904333122116, 1.119328688267192)
A_2 = (3.775721221887101, 3.3771882547211556)
A_4 = (6.270118457207665, 2.667575248121338)
A_5 = (10.119231432400603, 2.3665273059274763)
A_6 = (14, 4)
f = Polynomial({A_1, A_2, A_3, A_4, A_5, A_6})
Fahrradgröße = 0.6 (slider from 0.4 to 1.2, step 0.1)
P = Point(f)
ny(x) = f(x) + (0.5 * Fahrradgröße / sqrt(1 + f'(x)^(2)))
nx(x) = x - ((0.5 * Fahrradgröße) * f'(x) / sqrt(1 + f'(x)^(2)))
e = Circle(P, (0.5 * Fahrradgröße))
a = Tangent(P, f)
c = OrthogonalLine(P, a)
C, D = Intersect(e, c)
M = If(y(D) > y(P), D, C)
P_1 = Root(sqrt((nx(x) - x(M))^(2) + (ny(x) - y(M))^(2)) - (1.3 * Fahrradgröße), x(P), x(P) + (2.5 * Fahrradgröße))
B: (x(P_1), f(x(P_1)))
g_4 = Circle(B, (0.5 * Fahrradgröße))
b = Tangent(B, f)
d = OrthogonalLine(B, b)
E, F = Intersect(g_4, d)
N = If(y(F) > y(B), F, E)
G = Midpoint(M, N)
G' = Rotate(G, 60*°, M)
l = Segment(G', M)
m_3 = Line(G, l)
i = Segment(M, G)
n = Line(G', i)
H_2 = Intersect(m_3, n)
a_1 = Ray(G, H_2)
h_4 = Circle(M, P)
k = Circle(N, B)
α = Angle(G, M, G')
p = Segment(G', H_2)
r = Segment(H_2, N)
b_1 = Ray(G, G')
f_1(x) = sqrt((nx(x) - x(M))^(2) + (ny(x) - y(M))^(2)) - (1.3 * Fahrradgröße)
s = Circle(G, (0.8 * Fahrradgröße))
I = Intersect(s, b_1)
J = Intersect(s, a_1)
j = Segment(J, G)
q = Line(J, p)
e_1 = Circle(M, (0.1 * Fahrradgröße))
g_1 = Circle(G, (0.15 * Fahrradgröße))
h_1 = Ray(G, M)
k_1 = Circle(G, (1.95 * Fahrradgröße))
O = Intersect(k_1, h_1)
i_1, j_1 = Tangent(O, g_1)
Q_1, R = Intersect(e_1, j_1)
S, T = Intersect(e_1, i_1)
U = Intersect(g_1, i_1)
V = Intersect(g_1, j_1)
l_1 = Segment(Q_1, V)
m_1 = Segment(S, U)
H' = Rotate(H_2, 90*°, N)
H'_1 = Rotate(H_2, 260*°, N)
n_1 = Ray(N, H')
p_1 = Ray(N, H'_1)
q_1 = Circle(N, (0.53 * Fahrradgröße))
W = Intersect(q_1, n_1)
Z = Intersect(q_1, p_1)
r_1 = CircleArc(N, Z, W)
G'' = Rotate(G', 130*°, M)
β = Angle(G', M, G'')
G''_1 = Rotate(G', 280*°, M)
s_1 = Ray(M, G'')
t_1 = Ray(M, G''_1)
G''_2 = Rotate(G', (-4 * x(P)), G)
γ = Angle(G', G, G''_2)
a_2 = Line(G''_2, G)
e_2 = Circle(G, (0.2 * Fahrradgröße))
C_1, D_1 = Intersect(e_2, a_2)
b_2 = Segment(D_1, C_1)
f_2 = Line(C_1, i)
g_2 = Line(D_1, i)
h_2 = Circle(C_1, (0.05 * Fahrradgröße))
E_1, F_1 = Intersect(h_2, f_2)
i_2 = Segment(E_1, F_1)
k_2 = Circle(D_1, (0.05 * Fahrradgröße))
G_1, H_1 = Intersect(k_2, g_2)
j_2 = Segment(G_1, H_1)
p_2(x) = 3 - (x - 6)^(2) / 12 - (x - 6)^(3) / 54 + (2 * sin(x))
X_p: (x(P), 0)
n_2 = Segment(P, X_p)
H = Point(f)
t_2 = Line(P, H)
a_3 = OrthogonalLine(H, xAxis)
b_3 = OrthogonalLine(P, a_3)
J_1 = Intersect(a_3, b_3)
poly1, breit, hoch, j_3 = Polygon(P, J_1, H)
m_sH: (x(H), (y(H) - y(P)) / (x(H) - x(P)))
tP = Tangent(P, f)
m_P = Slope(tP)
A: (x(P), Slope[tP])
m = Segment((x(P) + 1, y(P)), (x(P) + 1, y(P) + Slope[tP]))
u = false
Q = Point(xAxis)
M_1 = Point(xAxis)
N_1 = Point(xAxis)
O_1 = Point(xAxis)
e_3 = OrthogonalLine(Q, xAxis)
g_3 = OrthogonalLine(M_1, xAxis)
h_3 = OrthogonalLine(N_1, xAxis)
i_3 = OrthogonalLine(O_1, xAxis)
q_5(x) = f'(x)
d_1 = Segment(A, X_p)
OrtVonA = Locus(A, P)
t = false
v = false
f_s(x) = f'(x)