θ

θ

Konstr. als Cissoide

r(x)=\frac{a}{\cos(x)}-2 a \cos(x)

Konstr. also Strophoide

Verbindung

Ende

Kongruenz

offen?

kleine Dreiecke

a = 2
r(x) = a / cos(x) - ((2 * a) * cos(x))
θ = 0 (slider from 0 to 6.28, step 0.1)
K: (θ, r(θ))
P: (r(θ); θ)
polarOrtP = Locus(P, θ)
c: (x - a)^(2) + y^(2) = a^(2)
b: x = a
Q = Point(c)
O = (0, 0)
d = Line(O, Q)
E = Intersect(b, d)
u = Vector(Q, E)
P' = Translate(O, u)
v = Vector(O, P')
CissoOrtP' = Locus(P', Q)
e = Segment(O, P)
P_n = Mirror(P, O)
f = Segment(O, P_n)
K': (θ, 0)
g = Segment(K', K)
h = CurveCartesian((r(t) * cos(t)), (r(t) * sin(t)), t, 0, θ)
A = Point(xAxis)
α = Angle(A, O, P)
β = Angle(A, O, P_n)
i = false
Q_s = Point(yAxis)
S = (-2, 0)
k = Circle(Q_s, O)
j = Ray(S, Q_s)
P_s, P'_s = Intersect(k, j)
stropho1 = Locus(P_s, Q_s)
stropho2 = Locus(P'_s, Q_s)
l = false
m = OrthogonalLine(Q, xAxis)
B = Intersect(j, m)
n = LineBisector(O, E)
C = Intersect(n, m)
o = false
p = Line(C, S)
q = false
D = Mirror(Q_s, n)
p' = Mirror(p, n)
F = Point(yAxis)
t = Line(O, p)
G = Intersect(t, b)
a_1 = Line(G, xAxis)
H = Intersect(p, yAxis)
S' = Mirror(S, yAxis)
w = false
s = LineBisector(E, O)
Vieleck1 = Polygon({S, O, Q_s})
Vieleck2 = Polygon({O, S', G})
c_1 = Segment(S', Q)
Vieleck3 = Polygon({S, P', O})
Vieleck4, s', e_1, q_1 = Polygon(E, Q, S')
b_1 = false
d_1 = Line(S', j)