https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 9.4.2.4: S.283
www.kurven-erkunden-und-verstehen.de

Ha 2016

t

t = 2.2776546738526 (slider from 0 to π, step π / 40)
a = 3
ys: ((1 / 6 * a) * (sin(t) + sin((2 * t)) - sin((3 * t))))
yk: (2 * ys)
xs: ((1 / 6 * a) * (1 + cos(t) + cos((2 * t)) - cos((3 * t))))
xk: (2 * xs) - 1
b = CurveCartesian((a / 3 * ((2 * cos(t)) - cos((2 * t)))), (a / 3 * ((2 * sin(t)) - sin((2 * t)))), t, 0, (2 * π))
A = (1, 0)
O_1 = (0, 0)
O: (0, 0)
B = Point(xAxis)
c = CurveCartesian((3 / 2 * cos(t)) - cos((3 * t)) / 2, (3 / 2 * sin(t)) - sin((3 * t)) / 2, t, 0, (2 * π))
l = Segment(((-a), 0), (1, 0))
d = false
e: ((a - (3 * x))^(4) * (a + (6 * x))^(2)) + (2916 * y^(6)) = (((18 * (a - (3 * x))) * (a^(3) - ((9 * a^(2)) * x) - ((54 * a) * x^(2)) + (162 * x^(3)))) * y^(2)) + ((243 * (a^(2) + ((12 * a) * x) - (36 * x^(2)))) * y^(4))
K: (xk, yk)
S: (xs, ys)
j: ((a - (3 * x))^(3) * (a + x)) + ((18 * (a^(2) - (3 * x^(2)))) * y^(2)) = (27 * y^(4))
p(x) = (tan(t) * (x - a / 3))
q: y = (tan((3 * t / 2)) * (x - a / 3))
f_1 = OrthogonalLine(S, q)
Q: ((a / 3 * ((2 * cos(t)) - cos((2 * t)))), (a / 3 * ((2 * sin(t)) - sin((2 * t)))))
B' = Rotate(B, t, A)
α = Angle(B, A, B')
f = Ray(Q, K)
C, D, G, H = Intersect(j, f)
E = Intersect(l, xAxis)
h = Segment(Q, D)
Q' = Mirror(Q, xAxis)
Q'_1 = Mirror(Q, xAxis)
D' = Mirror(D, xAxis)
h' = Segment(Q'_1, D')
g' = Segment(Q', D')
g = Segment(Q, D)
i = Tangent(Q, b)