t

t

4 π

4 π

4 π

4 π

4  π

Achimedische Spirale

4 π

4  π

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 9.3.3.1: S.274
www.kurven-erkunden-und-verstehen.de

Ha 2016

O = (0, 0)
a = 2
c = Circle(O, a)
A: (a, 0)
t = 8.5 (slider from -5 to 20, step 0.1)
Q = Rotate(A, t, O)
α = Angle(A, O, Q)
d = CircleArc(O, A, Q)
b = Segment(O, Q)
e = OrthogonalLine(Q, b)
f = Circle(Q, d)
P', C = Intersect(f, e)
g = Segment(Q, P')
h = CurveCartesian((a * (cos(t) + (t * sin(t)))), (a * (sin(t) - (t * cos(t)))), t, 0, 20)
i = OrthogonalLine(Q, xAxis)
j = OrthogonalLine(P', i)
B = Intersect(i, j)
k = Segment(Q, B)
l = Segment(B, P')
D = Point(i)
β = Angle(D, Q, P')
m: x = a
n: x = (-a)
p: y = a
q: y = (-a)
E, F, G, H, I, J = Intersect(p, h)
K, L, M, N, R, S = Intersect(n, h)
T, U, V, W, Z, A_1 = Intersect(m, h)
r = Segment(E, G)
s = Segment(G, I)
B_1, C_1, D_1, E_1, F_1 = Intersect(q, h)
f_1 = Segment(D_1, B_1)
g_1 = Segment(U, W)
G_1 = Point(m)
P: ((a * (cos(t) + (t * sin(t)))), (a * (sin(t) - (t * cos(t)))))
h_1 = Segment(M, K)
u = false
i_1 = Segment(R, M)
j_1 = Segment(F_1, D_1)
o = CurveCartesian(((a * (theta + π / 2)) * cos(theta)), ((a * (theta + π / 2)) * sin(theta)), theta, (-π) / 2, 10)
v = false