Kardioide aus der Reflexion konstruiert
Author: Dörte Haftendorn
Date: Juli 05

P konstruieren

Ort

Ha 09

Kardioide, aus der Reflexion konstruieren

Katakaustik

Erklärungen auf einer Extraseite
Kardioide-und-reflexion.pdf

B = Intersect(xAxis, yAxis)
A = Point(xAxis)
c = Circle(A, B)
Q_1 = Point(c)
g = Line(Q_1, B)
k = 8 (slider from 0 to 12, step 0.1)
kr: (x - x(Q_1))^(2) + (y - y(Q_1))^(2) = k^(2)
C, P_1 = Intersect(kr, g)
Leine = Segment(Q_1, P_1)
loc1 = Locus(P_1, Q_1)
L: (-2 k, 0)
d = Circle(A, L)
D = Point(d)
R = Segment(D, A)
b = Segment(D, L)
D' = Mirror(D, R)
L' = Mirror(L, R)
b' = Segment(D', L')
e = Line(B, R)
E_1, Q = Intersect(c, e)
f = Circle(Q, k)
P, I = Intersect(f, e)
h = Segment(P, Q)
i = Segment(A, L')
j = Segment(D, L')
l = Line(A, L')
m = Segment(Q, L')
n = Line(L, B)
r = Segment(Q, A)
a = Segment(D, L)
p = false
q = false
F = Intersect(b', j)
J = Intersect(n, j)
s = Segment(D, J)
E = Point(d)
t = Segment(L, E)
a_1 = Segment(E, A)
L'_1 = Mirror(L, a_1)
E' = Mirror(E, a_1)
t' = Segment(L'_1, E')
G = Intersect(t', n)
b_1 = Segment(G, E)
c_1 = Segment(G, E)
d_1 = Segment(L, E)
e_1 = Segment(E, L'_1)