Scherung  bei Funktionen erklären
Author: Prof. Dr. Dörte Haftendorn

Urbilddreieck

Bildreieck

alle Konstruktionslinien

Urparabel

Bildparabel

Urpunkte B,C

Bildpunkte, B',C'

Tangente in P'

Definierende Gerade

α vergrößern

Ha 09

A = Point(xAxis)
a = OrthogonalLine(A, xAxis)
P = (4.002277178149962, 1.7514287529100947E-5)
b = OrthogonalLine(P, a)
F_P = Intersect(a, b)
c = Line(P, a)
α = 0 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
B'_1 = Rotate(P, α, F_P)
β = Angle(P, F_P, B'_1)
d = Ray(F_P, B'_1)
P' = Intersect(d, c)
e = Segment(F_P, P')
f = Segment(P, P')
g = Segment(F_P, P)
B = (2.2766073742758204, 1.5817140908205223)
C = (5.7309157472554375, 1.5786560833930061)
Vieleck1, n, p, q = Polygon(P, B, C)
B', h, i, j, E = scher(a, α, B)
C', k, l, m, G = scher(a, α, C)
Vieleck2, p'_1, d_1, f_1 = Polygon(B', C', P')
o = false
r = false
s = false
g_b(x) = y(P') * (x - x(B')) * (x - x(C')) / ((x(P') - x(B')) * (x(P') - x(C'))) + y(B') * (x - x(P')) * (x - x(C')) / ((x(B) - x(P')) * (x(B') - x(C'))) + y(C') * (x - x(P')) * (x - x(B')) / ((x(C') - x(P')) * (x(C') - x(B')))
g_u(x) = y(P) * (x - x(B)) * (x - x(C)) / ((x(P) - x(B)) * (x(P) - x(C))) + y(B) * (x - x(P)) * (x - x(C)) / ((x(B) - x(P)) * (x(B) - x(C))) + y(C) * (x - x(P)) * (x - x(B)) / ((x(C) - x(P)) * (x(C) - x(B)))
u = true
v = true
w = true
z = true
a_1 = Tangent(P', g_b)
b_1 = false
t = Line(A, e)
c_1 = true
e_1 = Segment((x(B), 0.0), (x(B), y(B') - y(B)))
g_1 = Segment((x(C), 0.0), (x(C), y(C') - y(C)))
h_1 = Segment((x(P), 0.0), (x(P), y(P') - y(P)))
D = Extremum(g_u)

Tool: scher
Achse, Winkel,Punkt
Input: a, α, P
Output: P', f, e, g, F_P

b = OrthogonalLine(P, a)
F_P = Intersect(a, b)
F_P = Intersect(a, b)
c = Line(P, a)
B' = Rotate(P, α, F_P)
d = Ray(F_P, B')
P' = Intersect(d, c)
e = Segment(F_P, P')
f = Segment(P, P')
g = Segment(F_P, P)