violette Topfblume Strophoide und Konchoide

Konstr. rote Topfblume

Enkel-Kurve der roten Topfblume

rote Topfblume

Enkel-Kurve der violetten Topfblume

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 5.1.3.2 Aufgabe 5.1 S. 130
www.kurven-erkunden-und-verstehen.de

Ha 2017

a = 2.013 (slider from -5 to 5, step 0.001)
O = (0, 0)
A: (0, (-a))
r = 2 (slider from 0 to 5, step 0.01)
c = Circle(A, r)
Q = Point(c)
d = Line(Q, O)
e = Circle(Q, A)
B, F = Intersect(e, d)
Ortslinie1 = Locus(F, Q)
f = OrthogonalLine(A, yAxis)
g_2 = OrthogonalLine(Q, f)
E = Intersect(g_2, f)
h = Line(E, O)
P, P' = Intersect(e, h)
Ortslinie2 = Locus(P', Q)
Ortslinie3 = Locus(P, Q)
i = Segment(Q, E)
j = Segment(A, E)
Vieleck1, q, a_1, d_1 = Polygon(A, E, Q)
G = Intersect(e, d, 1)
Ortslinie4 = Locus(G, Q)
k = Segment(P', P)
l = false
m = true
n = Segment(O, G)
g: y = (y(Q) / x(Q) * x)
t: x(Q)^(2) + (y(Q) + a)^(2) - r^(2)
Text1: "t= " + t + ""
v: (a * ((a^(3) * (x^(2) + y^(2))) + (((4 * a^(2)) * y) * (x^(2) + y^(2))) + (((4 * y) * (x^(2) + y^(2))) * ((-2 * r^(2)) + x^(2) + y^(2))) + ((2 * a) * (x^(4) - ((2 * r^(2)) * y^(2)) + ((4 * x^(2)) * y^(2)) + (3 * y^(4)))))) = (((4 * r^(2)) - x^(2) - y^(2)) * (x^(2) + y^(2))^(2))
w: (((4 * a) * y) * (x^(2) + y^(2))^(2)) + (y^(2) * (x^(2) + y^(2))^(2)) + (a^(4) * ((4 * x^(2)) + y^(2))) + ((4 * a^(3)) * (((3 * x^(2)) * y) + y^(3))) + ((2 * a^(2)) * ((2 * x^(4)) + ((7 * x^(2)) * y^(2)) + (3 * y^(4)))) = (((4 * r^(2)) * y^(2)) * (a + y)^(2))
o: (((4 * a) * y) * (x^(2) + y^(2))^(2)) + (y^(2) * (x^(2) + y^(2))^(2)) + (a^(4) * ((4 * x^(2)) + y^(2))) + ((4 * a^(3)) * (((3 * x^(2)) * y) + y^(3))) + ((2 * a^(2)) * ((2 * x^(4)) + ((7 * x^(2)) * y^(2)) + (3 * y^(4)))) = (((4 * r^(2)) * y^(2)) * (a + y)^(2))
u = Vector(O, P)
Q' = Translate(Q, u)
p = Vector(Q, Q')
Ortslinie5 = Locus(Q', Q)
s = Vector(O, P')
Q'_1 = Translate(Q, s)
u_1 = Vector(Q, Q'_1)
Ortslinie6 = Locus(Q'_1, Q)
b_1 = false
v_1 = Vector(O, F)
Q'_2 = Translate(Q, v_1)
w_1 = Vector(Q, Q'_2)
Ortslinie7 = Locus(Q'_2, Q)
c_1 = Vector(O, G)
Q'_3 = Translate(Q, c_1)
e_1 = Vector(Q, Q'_3)
g_1 = Segment(O, P')
h_1 = true
i_1 = false
b = false