r(x)

K=(θ, r(θ))

θ

r(θ)

P=(r(θ); θ)

r(θ)

θ

P_n=(|r(θ)|;θ)

θ

P

r_1(θ)=2\,\sqrt{θ}+1

r_2(θ)=-2\,\sqrt{θ}+1

Lockwood-
Spirale

Ha 2016

c = 0.8 (slider from -5 to 5, step 0.01)
a = 1 (slider from -5 to 5, step 0.001)
r(x) = (a * sqrt(x)) + 1
θ = -15.25 (slider from -20 to 20, step 0.01)
K: (θ, r(θ))
T: (x(K), 0)
O: (0, 0)
b = Segment(K, T)
P: (r(θ); θ)
d = Segment(P, O)
A = Point(xAxis)
α = Angle(A, O, P)
P_n = Mirror(P, O)
β = Angle(A, O, P_n)
e = Segment(O, P_n)
anf = 0
end = 17.2
rn(x) = (-2 * sqrt(x)) + 1
f = CurveCartesian((r(t) * cos(t)), (r(t) * sin(t)), t, anf, end)
g = CurveCartesian((rn(t) * cos(t)), (rn(t) * sin(t)), t, anf, end)
h: y = 3
tt = -13.25 (slider from -20 to 5, step 0.01)
KK: (tt, r(tt))
PP: (r(tt); tt)
B = (-10, -5)
C = Point(r)
i = CurveCartesian((((-r(t)) + 2) * cos(t)), (((-r(t)) + 2) * sin(t)), t, anf, (2 * end))