Der Satz des Pythagoras
Author: marnie

Der Satz des Pythagoras - eine mögliche Begründung

Rechne nach:

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Aufgabe:
Bewege die Figur und vergleiche dabei die Rechnung rechts.
Was stellst du fest? Mache ein allgemeingültige Aussage.

A = (-4.635818181818181, 0.5398181818181824)
C = (-1.9078181818181812, 2.3218181818181822)
g = Line(A, C)
h = OrthogonalLine(C, g)
B = Point(h)
c = Segment(B, A)
a = Segment(C, B)
b = Segment(A, C)
γ = Angle(A, C, B)
e = OrthogonalLine(A, b)
f = OrthogonalLine(C, b)
k = Circle(A, C)
D, E = Intersect(k, e)
i = Line(E, b)
F = Intersect(i, f)
n = OrthogonalLine(B, a)
p = Circle(B, C)
G, H = Intersect(p, n)
q = OrthogonalLine(C, a)
r = OrthogonalLine(H, n)
I = Intersect(r, q)
j = OrthogonalLine(A, c)
l = OrthogonalLine(B, c)
s = Circle(A, B)
J, K = Intersect(s, j)
m = OrthogonalLine(K, j)
L = Intersect(m, l)
poly1, b1, b2, b3, b4 = Polygon(A, C, F, E)
Textpoly1: "Fläche " + (Name[A]) + (Name[C]) + (Name[F]) + (Name[E]) + " = " + poly1
poly2, a1, a2, a3, a4 = Polygon(C, B, H, I)
Textpoly2: "Fläche " + (Name[C]) + (Name[B]) + (Name[H]) + (Name[I]) + " = " + poly2
poly3, c2, c3, c4, c1 = Polygon(A, K, L, B)
Textpoly3: "Fläche " + (Name[A]) + (Name[K]) + (Name[L]) + (Name[B]) + " = " + poly3
T5: "Fläche " + (Name[A]) + (Name[C]) + (Name[F]) + (Name[E]) + " = " + poly1
T6: "Fläche " + (Name[C]) + (Name[B]) + (Name[H]) + (Name[I]) + " = " + poly2
T7: "Fläche " + (Name[A]) + (Name[K]) + (Name[L]) + (Name[B]) + " = " + poly3