Bärenkasten der Parabel mit Scherung für Archimedes
Author: Prof. Dr. Dörte Haftendorn

gerader Kasten

schräger Kasten

Gescherte Parabel

Ha 09

Parabelausschöpfung des Archimedes

Großes Dreieck D_0

kleines gerades Dreieck D_k

D_1=\frac{D_0}{8}

D_1=D_k

D_1'

D_1+D_1'=\frac{D_0}{4}

D_{2}+D_2'=\frac{D_1}{4}

Und so weiter

D_2

k = 0.25
f(x) = k * x^(2.0)
P = Point(f)
P': (x(P), 0.0)
r = 2
c = Circle(P', r)
B_1, C = Intersect(c, xAxis)
a = OrthogonalLine(B_1, xAxis)
b = OrthogonalLine(C, xAxis)
A = Intersect(f, a)
B = Intersect(f, b)
d = Segment(A, B)
e = Tangent(P, f)
ta(x) = Slope[e] * (x - x(P)) + y(P)
p(x) = f(x) - ta(x)
D = Intersect(p, a)
E = Intersect(p, b)
G = Intersect(ta, a)
H = Intersect(ta, b)
Vieleck4, g_1, a_2, b_2, h_1 = Polygon(G, A, B, H)
Vieleck5, b_3, c_1, e_2, d_2 = Polygon(B_1, C, E, D)
m = false
n = false
q = false
M = Midpoint(A, B)
s = Segment(M, P)
D_1, b_4, a_3, p_2 = Polygon(A, P, B)
D_k, e_3, d_3, p'_1 = Polygon(D, P', E)
B' = Mirror(B, yAxis)
D_0, a_4, b', b_5 = Polygon(B', B, A)
h = true
t = false
A' = Mirror(A, yAxis)
P'_1 = Mirror(P, yAxis)
B'_1 = Mirror(B, yAxis)
Vieleck6, b'_1, a', p'_2 = Polygon(A', P'_1, B'_1)
v = true
F: (x(A) / 2.0 + x(P) / 2.0, f(x(A) / 2.0 + x(P) / 2.0))
Vieleck1, p_1, a_1, f_1 = Polygon(A, F, P)
g = false