Gerüst zeigen

Vektoren zeigen

Für t=0 wird die
Gorono-Lemniskate
genau erreicht.

BewegungsWege

Man kann Cn, An und t animieren

Hein Mück un sin Fru

ziehe an An, Cn oder t 

a_{1}: 1
Gerono:=x^(4) = (a_{1} * (x^(2) - y^(2)))
b_{1}: sqrt(a_{1}) / 2
f: y = b_{1}
A: (1, 0)
g: x = sqrt(a_{1})
h: y = (1 / 2 * x)
F = Point(h)
C: (3 / 4, -3 / 4)
D: (1 / 2, -1 / 2)
E: (0, 0)
B = (1, -0.5)
Dn = (-16.176701694725857, 6.915705292385883)
En = (-10.168620585533244, -0.031138490118091652)
I = (8.75, -10.5)
I' = Mirror(I, xAxis)
maul = Segment(I', I)
K = Point(maul)
maulu = Segment(K, I)
An = Point(maulu)
a = Vector(A, An)
G = Point(xAxis)
G' = Mirror(G, yAxis)
Bn = (-16.75, -10)
b = Vector(B, Bn)
H = (0.3984216307292628, -8.702517229124597)
J = (20.632570845641425, -8.555181191151934)
Flosse = Segment(H, J)
Cn = Point(Flosse)
c = Vector(C, Cn)
d = Vector(D, Dn)
e = Vector(E, En)
t = 1 (slider from 0 to 1, step 0.01)
At: A + (t * a)
Bt: B + (t * b)
Ct: C + (t * c)
Dt: D + (t * d)
Et: E + (t * e)
NG(s) = (1 + s^(2))^(2)
Z1(s) = (1 - s)^(4)
Z2(s) = ((4 * (1 - s)^(3)) * s)
Z3(s) = ((8 * (1 - s)^(2)) * s^(2))
Z4(s) = ((8 * (1 - s)) * s^(3))
Z5(s) = (4 * s^(4))
i = CurveCartesian((x(At) * Z1(s) / NG(s)) + (x(Bt) * Z2(s) / NG(s)) + (x(Ct) * Z3(s) / NG(s)) + (x(Dt) * Z4(s) / NG(s)) + (x(Et) * Z5(s) / NG(s)), (y(At) * Z1(s) / NG(s)) + (y(Bt) * Z2(s) / NG(s)) + (y(Ct) * Z3(s) / NG(s)) + (y(Dt) * Z4(s) / NG(s)) + (y(Et) * Z5(s) / NG(s)), s, 0, 1)
i' = Mirror(i, xAxis)
i'_{1} = Mirror(i, yAxis)
p: y = (-x)
i'' = Mirror(i', yAxis)
j = false
k = false
An' = Mirror(An, xAxis)
l = OrthogonalLine(I, xAxis)
At' = Mirror(At, xAxis)
q = Semicircle(At, At')
L = (-6.230406792093831, -4.640581996523027)
K' = Mirror(K, xAxis)
maulo = Segment(K', I')
M = (7.8869148311549715, 9.731993312319927)
N = (13.72336284525661, -6.834560204956543)
m = Segment(M, N)
i'_{2} = Mirror(i, m)
i''_{1} = Mirror(i', m)
q' = Mirror(q, m)
Gerono' = Mirror(Gerono, m)
P = (22.10593122536804, 8.830471289622158)
Gerono'' = Dilate(Gerono', 2, P)
n = false
Q = (-16.996233440185556, 27.285629028261273)
r = Segment(A, B)
s = Segment(B, C)
f_1 = Segment(A, B)
g_1 = Segment(B, C)
h_1 = Segment(A, B)
i_1 = Segment(B, C)
j_1 = Segment(C, D)