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

Scherung

gerader Kasten

schräger Kasten

Scherachse

Gescherte Parabel

Ha 09

Parabel und ihre Bärenkästen

k = 0.25
f(x) = k * x^(2.0)
P = Point(f)
P': (x(P), 0.0)
r = 3
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)
F = Intersect(ta, xAxis)
g = OrthogonalLine(F, xAxis)
l = OrthogonalLine(E, g)
I = Intersect(g, l)
Vieleck1, d_1, a_1, i = Polygon(A, I, D)
Vieleck2, b_1, i_1, e_1 = Polygon(I, E, B)
j = false
Vieleck3, p_1, f_1, p' = Polygon(F, P', P)
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 = true
o = false
q = false
M = Midpoint(A, B)
s = Segment(M, P)