i.A. nicht konstant,
auch nicht bei F=A

Booth'sche Ovale

Booth'sche Lemniskaten

Cassini'sche Kurven

Abstandsprodukt

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 4.4.2: Aufgabe 4.7 S. 116
www.kurven-erkunden-und-verstehen.de

Ha 2017

c = 4 (slider from 0 to 10, step 0.1)
s = 1.4 (slider from -5 to 5, step 0.1)
boL: (x^(2) + y^(2))^(2) = (c^(2) * x^(2)) - (s^(2) * y^(2))
boO: (x^(2) + y^(2))^(2) = (c^(2) * x^(2)) + (s^(2) * y^(2))
A = Point(xAxis)
A' = Mirror(A, yAxis)
B = Point(boO)
f = Segment(A', B)
g = Segment(A, B)
h: (f * g)
Text1: "" + f + "*" + g + "=" + h + ""
ee: sqrt((c^(2) - s^(2)) / 2)
kk: sqrt((c^(2) + s^(2)) / 2)
i: kk^(2)
cass: (x^(2) + y^(2))^(2) = ((2 * ee^(2)) * (x^(2) - y^(2))) + kk^(4) - ee^(4)
F: (ee, 0)
F': ((-ee), 0)
a = false
b = false