Archimedes Quadratur der Parabel
Author: Prof. Dr. Dörte Haftendorn
Date: Juli 05

Ha 05

Archimedes

Die Fläche der grünen Dreiecke

ist zusammen ein Viertel

des blauen Dreiecks

p(x) = 0.25 * x^(2.0)
A = Point(p)
B = Point(p)
a = Segment(A, B)
b = LineBisector(A, B)
M = Intersect(a, b)
c = OrthogonalLine(M, xAxis)
C = Intersect(p, c)
d = Tangent(C, p)
e = OrthogonalLine(A, xAxis)
f = OrthogonalLine(B, xAxis)
D = Intersect(e, d)
E = Intersect(f, d)
F = Midpoint(D, C)
G = Midpoint(D, A)
H = Midpoint(D, G)
I = Midpoint(G, A)
J = Midpoint(C, E)
g = Line(I, d)
h = Line(G, d)
i = Line(H, d)
j = Line(F, yAxis)
k = Line(J, yAxis)
P, d_1, e_1, b_1, a_1 = Polygon(D, E, B, A)
l = Segment(A, C)
K = Intersect(j, i)
m = Line(I, K)
L = Intersect(d_1, d)
N = Intersect(m, d)
n = Segment(I, N)
O = Intersect(g, f)
Q = Intersect(h, f)
R = Intersect(i, f)
S = Intersect(b_1, a)
T = Intersect(j, a)
U = Intersect(b_1, a)
V = Intersect(k, a)
q = Segment(T, F)
r = Segment(M, C)
s = Segment(V, J)
t = Segment(I, O)
c_1 = Segment(G, Q)
f_1 = Segment(H, R)
g_1 = Segment(I, N)
W_1, k_1, a_2, c_2 = Polygon(A, C, K)
Z = Intersect(s, f_1)
P_1, b_3, c_4, z = Polygon(C, Z, B)
Y, b_2, a_3, c_3 = Polygon(A, C, B)
h_1 = OrthogonalLine(C, xAxis)
i_1 = Line(N, I)
W = Intersect(i_1, h_1)
j_1 = Segment(N, W)
l_1 = Segment(C, W)