Kardioide als Katakaustik
Author: Prof. Dr. Dörte Haftendorn
Date: Jan 09

Reflexionskurven heißen auch Katakaustiken

kleiner Kreis

Ort

Ha 09

Katakaustik

Kardioide und Refklexion

Baum

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