Das Heron'sche (Babylonische) Wurzelziehen
Author: Andreas Lindner

Bewege den blauen Punkt auf der x-Achse.

x-Wert

y-Wert

Rechteck

Mittelwert

Iterationsformel:

x_{n+1} \, = \,  \frac{ 1 }{2} · (x_n+\frac{ A }{x_n } )

A = 2
a = Ray((0.0, 0.0), (5.0, 0.0))
P = Point(a)
A2: x(P)
B2: A / A2
C2: (A2 + B2) / 2.0
A3: C2
B3: A / A3
C3: (A3 + B3) / 2.0
O = (0, 0)
D2, b, c, d, e = Polygon(O, (A2, 0.0), (A2, B2), (0.0, B2))
D3, E3, F3, G3, H3 = Polygon(O, (A3, 0.0), (A3, B3), (0.0, B3))
A4: C3
B4: A / A4
C4: (A4 + B4) / 2.0
D4, E4, F4, G4, H4 = Polygon(O, (A4, 0.0), (A4, B4), (0.0, B4))
A5: C4
B5: A / A5
C5: (A5 + B5) / 2.0
D5, E5, F5, G5, H5 = Polygon(O, (A5, 0.0), (A5, B5), (0.0, B5))
Text3: "A = " + A
Text4: "x_1 = " + (x(P))