Ideal: (5.23, 4.13 )

\textcolor{#009900}

Satz von Schwarz ?

Mα

α

Mβ

β

\copyright \; Werner Knobloch, 2011

(p_0z/a_0z)  =

+10

-10

-10

+10

+10

-10

nur Dokumentation

nur Dokumentation

nur Dokumentation

nur Dokumentation

nur Dokumentation

Einfarbig / Netz

Funktionsgebirge

\textcolor{#00ffff}

\textcolor{#ff00ff}

nx :

ny :

opti: α = 228° /  β = 315°

opt: Sicht ( 3.9, 5.6 ) , α = 228° /  β = 315°

opti: α = 228° /  β = 315° /  γ = 0°

nxy :

Sicht = (3.92, 5.56)
x_{Sicht}: ((180 * x(Sicht) / π))°
Funktion = 1 (slider from 1 to Fmax, step 1)
Vorgabe(x, y) = (0.1 * (y^(3) - ((3 * y) * x^(2)))) + 1.5
Funktionsliste: {Vorgabe(x, y), (y * sin(x - π)) + (x * sin(y - π)), ℯ^((-x^(2)) - y^(2)) + 1, (((9 * x) * y) * ℯ^((-x^(2)) - y^(2))), ((2 * sin(x)) * cos(y)), ((2 * sin((1.2 * x))) * cos((1.2 * y))), ((-2.5) * cos(sqrt(x^(2) + y^(2)) - π / 2)) + 3, (2.5 * cos(sqrt(x^(2) + y^(2)) - π / 2)), (0.8 * sin(x^(2) + y^(2)))}
f = Element(Funktionsliste, Funktion)
f_y = Derivative(f, y)
f_{yx} = Derivative(f_y, x)
Iltis2: "f_{yx} =   " + (LaTeX[f_{yx}]) + ""
f_x = Derivative(f, x)
f_{xy} = Derivative(f_x, y)
Iltis1: "f_{xy} = " + (LaTeX[f_{xy}]) + "  "
Trennebenenhöhe = 2.8 (slider from 0 to 20, step 0.1)
Koordinatenebenen_1: (Trennebenenhöhe * {{-1, -1, 0}, {1, -1, 0}, {1, 1, 0}, {-1, 1, 0}, {-1, 0, -1}, {1, 0, -1}, {1, 0, 1}, {-1, 0, 1}, {0, -1, -1}, {0, 1, -1}, {0, 1, 1}, {0, -1, 1}})
Zoom = 1.1 (slider from 0.1 to 2, step 0.1)
I = (1, 0)
i = Vector(I)
J = (0, 1)
j = Vector(J)
α_{Regler} = 3.9793506945470716 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
γ_{Regler} = 0 rad (slider from 0*° to 6.283185307179586, step 0.017453292519943295)
β_{Regler} = 5.497787143782138 rad (slider from 0*° to 360*°, step 1*°)
y_{Sicht}: ((180 * y(Sicht) / π))°
β_{Sicht}: y_{Sicht}
Kompass_r = 0.9 (slider from 0.2 to 2, step 0.05)
Kompass_A = (-11.334567425064098, -4.044883424587474)
Kompass_B: (x(Kompass_A) + (3.5 * Kompass_r), y(Kompass_A))
Kompass_C: (x(Kompass_B), y(Kompass_A) + (3 * Kompass_r))
Steuerung = 2 (slider from 1 to 3, step 1)
γ = If(Steuerung ≟ 1, γ_{Regler}, 0)
Kompass_{Mittenkorrektur} = If(Steuerung ≟ 2, ((-0.4) * Kompass_r), 0)
Kompass_{Mitte}: (x((Kompass_A + Kompass_C) / 2), y((Kompass_A + Kompass_C) / 2) + Kompass_{Mittenkorrektur})
Kompass_Iα: Kompass_{Mitte} + (((-1.00088) * Kompass_r), (1.27226 * Kompass_r))
Kompass_{Vertikale} = Line(Kompass_Iα, yAxis)
Kompass_c = Circle(Kompass_Iα, Kompass_r / 2)
Kompass_Mα = Point(Kompass_c)
Kompass_Eα = Intersect(Kompass_c, Kompass_{Vertikale}, 2)
α_{Sicht}: x_{Sicht}
Kompass_α = Angle(Kompass_Eα, Kompass_Iα, Kompass_Mα)
α = If(Steuerung ≟ 1, α_{Regler}, If[Steuerung ≟ 2, Kompass_α, α_{Sicht}])
e_3: ((-sin(γ)) * i) - ((sin(α) * cos(γ)) * j)
Kompass_{transl} = Vector((0, 0), (2, 0))
Kompass_Eβ = Translate(Kompass_Eα, Vector[(Kompass_r * Kompass_{transl})])
Kompass_{c'} = Translate(Kompass_c, Vector[(Kompass_r * Kompass_{transl})])
Kompass_Mβ = Point(Kompass_{c'})
Kompass_Iβ = Translate(Kompass_Iα, Vector[(Kompass_r * Kompass_{transl})])
Kompass_β = Angle(Kompass_Mβ, Kompass_Iβ, Kompass_Eβ)
β = If(Steuerung ≟ 1, β_{Regler}, If[Steuerung ≟ 2, Kompass_β, β_{Sicht}])
e_2: (((-cos(γ)) * sin(β)) * i) + (((cos(α) * cos(β)) + ((sin(α) * sin(γ)) * sin(β))) * j)
e_1: ((cos(γ) * cos(β)) * i) + (((cos(α) * sin(β)) - ((sin(α) * sin(γ)) * cos(β))) * j)
Matrix_{e_1,e_2,e_3}: {{x(e_1), x(e_2), x(e_3)}, {y(e_1), y(e_2), y(e_3)}}
Matrix_{e_1,e_2,e_3,Zoom}: (Zoom * Matrix_{e_1,e_2,e_3})
Koordinatenebenen_2 = Sequence(Join[(Matrix_{e_1,e_2,e_3,Zoom} * {{Element[Element[Koordinatenebenen_1, j], 1]}, {Element[Element[Koordinatenebenen_1, j], 2]}, {Element[Element[Koordinatenebenen_1, j], 3]}})], j, 1, 12)
Koordinatenebenen_3 = PointList(Koordinatenebenen_2)
e_3Zoom: (Zoom * e_3)
e_2Zoom: (Zoom * e_2)
e_1Zoom: (Zoom * e_1)
D_2 = 4
C_2 = -2
nx = 12 (slider from 3 to 40, step 1)
ny = 12 (slider from 3 to 40, step 1)
ymax = 2.5 (slider from 0 to 20, step 0.1)
ymin: (-ymax)
Δ_y: (ymax - ymin) / ny
xmax = 2.5 (slider from 0 to 20, step 0.1)
xmin: (-xmax)
Δ_x: (xmax - xmin) / nx
A_{xy} = Element(Koordinatenebenen_3, 3)
A_{xz} = Element(Koordinatenebenen_3, 7)
A_{yz} = Element(Koordinatenebenen_3, 11)
B_{xy} = Element(Koordinatenebenen_3, 2)
B_{xz} = Element(Koordinatenebenen_3, 6)
B_{yz} = Element(Koordinatenebenen_3, 10)
C_{xz} = Element(Koordinatenebenen_3, 5)
C_{yz} = Element(Koordinatenebenen_3, 9)
D_{xy} = Element(Koordinatenebenen_3, 4)
D_{xz} = Element(Koordinatenebenen_3, 8)
D_{yz} = Element(Koordinatenebenen_3, 12)
C_{xy} = Element(Koordinatenebenen_3, 1)
Ebene_{xy}, i_{xy}, j_{xy}, k_{xy}, l_{xy} = Polygon(A_{xy}, B_{xy}, C_{xy}, D_{xy})
Ebene_{yz}, a_{yz}, b_{yz}, c_{yz}, d_{yz} = Polygon(A_{yz}, B_{yz}, C_{yz}, D_{yz})
Ebene_{xz}, a_{xz}, b_{xz}, c_{xz}, d_{xz} = Polygon(A_{xz}, B_{xz}, C_{xz}, D_{xz})
xmax_{Raster}: xmax + (floor((nx * 0.3)) * Δ_x)
ymax_{Raster}: ymax + (floor((ny * 0.3)) * Δ_y)
xmin_{Raster}: (-xmax_{Raster})
ymin_{Raster}: (-ymax_{Raster})
V_1: e_1Zoom
V_2: e_2Zoom
n_xRaster: round((xmax_{Raster} - xmin_{Raster}) / Δ_x)
n_yRaster: round((ymax_{Raster} - ymin_{Raster}) / Δ_y)
V_3: e_3Zoom
O = (0, 0)
m = Line(O, V_2)
y_{Achse} = Line(O, V_2)
x_{Achse} = Line(O, V_1)
z_{Achse} = Line(O, V_3)
Koordinatenebenen = true
Achsen = false
Matrix_{direkt}: {{(-cos(γ)), (-sin(γ)), 0}, {(sin(α) * sin(γ)), ((-sin(α)) * cos(γ)), cos(α)}}
Animation_α = false
Animation_γ = false
speed_α = If(Animation_α, 1, 0)
Kompass_D: (x(Kompass_A), y(Kompass_C))
Kompass_{Vieleck}, kompass_a, kompass_b, kompass_c, kompass_d = Polygon(Kompass_A, Kompass_B, Kompass_C, Kompass_D)
Kompass_e: (x - x(Kompass_{Mitte}))^(2) + (y - y(Kompass_{Mitte}))^(2) / sin(α)^(2) = Kompass_r^(2)
Kompass_d: (x - x(Kompass_{Mitte}))^(2) + (y - y(Kompass_{Mitte}))^(2) / cos(α)^(2) = Kompass_r^(2)
Kompass_g: (x - x(Kompass_{Mitte}))^(2) + (y - y(Kompass_{Mitte}))^(2) = Kompass_r^(2)
Kompass_ax = Translate(Vector[(Kompass_r * e_1)], Kompass_{Mitte})
Kompass_ay = Translate(Vector[(Kompass_r * e_2)], Kompass_{Mitte})
Kompass_az = Translate(Vector[(Kompass_r * e_3)], Kompass_{Mitte})
Kompass_{Tβ} = Text("β =" + γ + "", Kompass_B + (-1, 0.1))
Kompass_{Tα} = Text("α =" + α + "", Kompass_A + (0.15, 0.1))
Raster_x = Sequence(Segment[(xmin_{Raster} * V_1) + ((ymin_{Raster} + (k * Δ_y)) * V_2), (xmax_{Raster} * V_1) + ((ymin_{Raster} + (k * Δ_y)) * V_2)], k, 0, n_yRaster)
Raster_y = Sequence(Segment[(ymin_{Raster} * V_2) + ((xmin_{Raster} + (k * Δ_x)) * V_1), (ymax_{Raster} * V_2) + ((xmin_{Raster} + (k * Δ_x)) * V_1)], k, 0, n_xRaster)
S_3z = 0
S_2y = 0
S_1x = 0
Betrag_{3D}(x, y, z) = sqrt(x^(2) + y^(2) + z^(2))
X_{10}: (10 * e_1Zoom)
X_{-10}: ((-10) * e_1Zoom)
w = Vector(X_{-10}, X_{10})
Y_{-10}: ((-10) * e_2Zoom)
Y_{10}: (10 * e_2Zoom)
Z_{10}: (10 * e_3Zoom)
Z_{-10}: ((-10) * e_3Zoom)
z = Vector(Y_{-10}, Y_{10})
b_1 = Vector(Z_{-10}, Z_{10})
Fmax = 9
Punkte = Sequence(Sequence[((xmin + (k * Δ_x)) * e_1Zoom) + ((ymin + (j * Δ_y)) * e_2Zoom) + (f(xmin + (k * Δ_x), ymin + (j * Δ_y)) * e_3Zoom), k, 0, nx], j, 0, ny)
Gitter_x = Sequence(Sequence[Segment[Element[Element[Punkte, l], k], Element[Element[Punkte, l], k + 1]], k, 1, nx], l, 1, ny + 1)
Gitter_y = Sequence(Sequence[Segment[Element[Element[Punkte, l], k], Element[Element[Punkte, l + 1], k]], k, 1, nx + 1], l, 1, ny)
Kacheln = Join(Sequence[Sequence[Element[{Polygon[Element[Element[Punkte, j], k], Element[Element[Punkte, j], k + 1], Element[Element[Punkte, j + 1], k + 1], Element[Element[Punkte, j + 1], k]]}, 1], k, 1, nx], j, 1, ny])
Deckkraft = 0.73 (slider from 0 to 1, step 0.01)
FarbBereichslänge = 2.3 (slider from 0 to Spanne, step 0.1)
Spanne = 10
FarbBereichsstart = 5.5 (slider from 0 to Spanne - FarbBereichslänge, step 0.1)
FarbElementarbereiche = 6 (slider from -5 to 6, step 1)
FarbKlassen = 35 (slider from 1 to 40, step 1)
Ordinatenfolge = Join(Sequence[Sequence[f(xmin + (k * Δ_x), ymin + (j * Δ_y)), k, 0, nx - 1], j, 0, ny - 1])
Intervallenden = Sequence((j * Spanne / FarbElementarbereiche), j, 0, FarbElementarbereiche)
Farbregler = 0.5 (slider from 0 to 0.5, step 0.01)
Farbe_{Rot}(x) = 1 + (Farbregler * ((-abs((Farbregler * (abs((2 / Element[Intervallenden, 3] * (x - Element[Intervallenden, 3]))) - 2 + abs((2 / Element[Intervallenden, 3] * (Element[Intervallenden, 5] - x))) - 2)))) + (Farbregler * (abs((2 / Element[Intervallenden, 3] * (x - Element[Intervallenden, 3]))) - 2 + abs((2 / Element[Intervallenden, 3] * (Element[Intervallenden, 5] - x))) - 2))))
Farbe_{Blau}(x) = 1 - Farbe_{Rot}(x - 1)
Farbe_{Grün}(x) = 1 - Farbe_{Rot}(x + 1)
Tangentialebene = 1.1 (slider from 0.1 to 5, step 0.1)
x_0 = -0.05 (slider from xmin to xmax, step 0.01)
y_0 = -0.35 (slider from ymin to ymax, step 0.01)
m_x: f_x(x_0, y_0)
m_y: f_y(x_0, y_0)
A_{Tangentialebene}: ((x_0 - Tangentialebene) * e_1Zoom) + (y_0 * e_2Zoom) + ((f(x_0, y_0) - (m_x * Tangentialebene)) * e_3Zoom)
B_{Tangentialebene}: ((x_0 + Tangentialebene) * e_1Zoom) + (y_0 * e_2Zoom) + ((f(x_0, y_0) + (m_x * Tangentialebene)) * e_3Zoom)
C_{Tangentialebene}: (x_0 * e_1Zoom) + ((y_0 - Tangentialebene) * e_2Zoom) + ((f(x_0, y_0) - (m_y * Tangentialebene)) * e_3Zoom)
D_{Tangentialebene}: (x_0 * e_1Zoom) + ((y_0 + Tangentialebene) * e_2Zoom) + ((f(x_0, y_0) + (m_y * Tangentialebene)) * e_3Zoom)
P_0: (x_0 * e_1Zoom) + (y_0 * e_2Zoom) + (f(x_0, y_0) * e_3Zoom)
Punkte_{x0} = Sequence(((x_0 * e_1) * Zoom) + (((ymin + (k * Δ_y)) * e_2) * Zoom) + ((f(x_0, ymin + (k * Δ_y)) * e_3) * Zoom), k, 0, ny)
Punkte_{y0} = Sequence((((xmin + (k * Δ_x)) * e_1) * Zoom) + ((y_0 * e_2) * Zoom) + ((f(xmin + (k * Δ_x), y_0) * e_3) * Zoom), k, 0, nx)
E_{Tangentialebene}: C_{Tangentialebene} + A_{Tangentialebene} - P_0
F_{Tangentialebene}: D_{Tangentialebene} + A_{Tangentialebene} - P_0
G_{Tangentialebene}: D_{Tangentialebene} - A_{Tangentialebene} + P_0
H_{Tangentialebene}: C_{Tangentialebene} - A_{Tangentialebene} + P_0
Tangetialebene_1, e_{tangentialebene}, f_{tangentialebene}, g_{tangentialebene}, h_{tangentialebene} = Polygon(E_{Tangentialebene}, F_{Tangentialebene}, G_{Tangentialebene}, H_{Tangentialebene})
Animation_β = false
R_x: {{1, 0, 0}, {0, cos(α), (-sin(α))}, {0, sin(α), cos(α)}}
R_y: {{cos(β), 0, (-sin(β))}, {0, 1, 0}, {sin(β), 0, cos(β)}}
R_z: {{cos(γ), (-sin(γ)), 0}, {sin(γ), cos(γ), 0}, {0, 0, 1}}
R_{xyz}: ((R_x * R_y) * R_z)
p_{xy}: {{1, 0, 0}, {0, 0, 1}}
R_{xyz}Proj: (p_{xy} * R_{xyz})
Tangentialfläche = true
Rasterebene = true
Gradientenvektor = true
Normalenvektor = true
Farbe = true
Einfarbig = false
PartielleAbleitung = true
Probepunkt = true
Probekachel = true
Gitterlinien = true
Gitterpunkte = false
P'_1: ((x_0 + m_x) * e_1) + ((y_0 + m_y) * e_2)
P_{x0y0}: (x_0 * e_1Zoom) + (y_0 * e_2Zoom)
Gradient = Vector(P_{x0y0}, P'_1)
Normalenrichtung: ((-f_x(x_0, y_0)) * e_1Zoom) - (f_y(x_0, y_0) * e_2Zoom) + e_3Zoom
Norm: sqrt(((-f_x(x_0, y_0)))^(2) + ((-f_y(x_0, y_0)))^(2) + 1)
Normale_x: (-f_x(x_0, y_0))
Normale_y: (-f_y(x_0, y_0))
Normale_z = 1
N: Normalenrichtung / Norm + (f(x_0, y_0) * e_3Zoom)
Normale = Vector(P_0, N)
Text6: "P_0= (" + (LaTeX[x_0]) + "," + LaTeX[y_0] + "," + LaTeX[LaTeX[f(x_0, y_0)]] + ")"
Text8 = Text(" β = " + β + " ", Kompass_B)
speed_β = If(Animation_β, 1, 0)
speed_γ = If(Animation_γ, 1, 0)
Wiesel1 = TableText({{1, 0, "f_x"}}, "cv()")
Wiesel2 = TableText({{0, 1, "f_y"}}, "cv()")
Wiesel3 = TableText({{"-f_x", "-f_y", 1}}, "cv()")
Wiesel4 = TableText({{Normale_x, Normale_y, Normale_z}}, "cv()")
Marder1 = TableText({{m_x, m_y, 0}}, "v()")
Marder2 = TableText({{"f_x", "f_y", 0}}, "v()")
Text5: "f_{xy} = " + (LaTeX[f_{xy}]) + "  "
Text10mitFarbe: "\mathbf \textcolor{#ff0000} {f_x= " + (LaTeX[f_x]) + " }"
Text7mitFarbe: "\mathbf \textcolor{#0000ff} {f_y= " + (LaTeX[f_y]) + "  }"
Text12: "  " + (LaTeX[Darkgreen]) + "{" + LaTeX[TableText[{{Iltis1, Iltis2, Iltis3}}, "v()"]] + "}"
Text7 = TableText({{Text10mitFarbe, Text7mitFarbe, Text12}}, "v")
Text1 = LaTeX(f, true, true)
Text4: "\mathbf " + (LaTeX[Violett]) + "\text{  }Gradient \cr  { " + LaTeX[TableText[{{Marder1 + " = " + Marder2}}, "h"]] + "}"
Text11: "\mathbf " + (LaTeX[Darkgreen]) + "{ Normalenrichtung:  \cr" + LaTeX[TableText[{{Wiesel1 + "\text{ x }" + Wiesel2 + "=" + Wiesel3 + "=" + Wiesel4}, "h"}]] + "}"
a = Segment(P_{x0y0}, P_0)
Gitter_{x0} = Sequence(Segment[Element[Punkte_{x0}, k], Element[Punkte_{x0}, k + 1]], k, 1, ny)
Gitter_{y0} = Sequence(Segment[Element[Punkte_{y0}, k], Element[Punkte_{y0}, k + 1]], k, 1, nx)
xTangente = Segment(C_{Tangentialebene}, D_{Tangentialebene})
yTangente = Segment(A_{Tangentialebene}, B_{Tangentialebene})
TimeOut = 1 (slider from 0 to 1, step 0.1)
n_{max} = 30
nx_{max}: n_{max}
ny_{max}: n_{max}
Farbtrafo(x) = FarbBereichsstart + (x * FarbBereichslänge / FarbKlassen)
Ordmax = Max(Ordinatenfolge)
Ordmin = Min(Ordinatenfolge)
Ordklasse(x) = round((FarbKlassen * (x - Ordmin) / abs(Ordmax - Ordmin))) + 1
Farbe_{Blauklasse}(x) = Farbe_{Blau}(Farbtrafo(Ordklasse(x)))
Farbe_{Grünklasse}(x) = Farbe_{Grün}(Farbtrafo(Ordklasse(x)))
Farbe_{Rotklasse}(x) = Farbe_{Rot}(Farbtrafo(Ordklasse(x)))
Blau = Sequence(Farbe_{Blauklasse}(Element[Ordinatenfolge, k]), k, 1, (nx * ny))
Grün = Sequence(Farbe_{Grünklasse}(Element[Ordinatenfolge, k]), k, 1, (nx * ny))
Rot = Sequence(Farbe_{Rotklasse}(Element[Ordinatenfolge, k]), k, 1, (nx * ny))
Textfeld1 = Textfield(nx)
Textfeld2 = Textfield(ny)
select_x = 4 (slider from 1 to nx, step 1)
select_y = 6 (slider from 1 to ny, step 1)
selectxy: select_x + ((select_y - 1) * nx)
Probe_{Kachel} = Element(Kacheln, selectxy)
Text10 = If(Steuerung > 2, LaTeX[Sicht, true, false], "")
A: (Sicht * 4.1)
Optipos = If(Steuerung > 2, Kompass_D + ((-0.3), 0.3), Kompass_D + (0, 0.3))
Text9 = Text(" α = " + α + " ", Kompass_C + (0, (-0.2)))
Sichtoptimum = true
Text14 = Text(Text10, (0.1, 0) + (Kompass_B + Kompass_C) / 2)
Text2 = Text(If[Steuerung  <  3, If[Steuerung  <  2, opti_1, opti_2], opti_3], Optipos)
nxy = 12 (slider from 3 to 40, step 1)
Textfeld3 = Textfield(nxy)
speedMα = If(Animation_α ∧ Steuerung ≟ 2, 1, 0)
speedMβ = If(Animation_β ∧ Steuerung ≟ 2, 1, 0)
Text13: "f(x,y)= " + f + ""
headline2: headline
K_{0101} = Element(Kacheln, 1)
K_{0102} = Element(Kacheln, 13)
K_{0103} = Element(Kacheln, 25)
K_{0104} = Element(Kacheln, 37)
K_{0105} = Element(Kacheln, 49)
K_{0106} = Element(Kacheln, 61)
K_{0107} = Element(Kacheln, 73)
K_{0108} = Element(Kacheln, 85)
K_{0109} = Element(Kacheln, 97)
K_{0110} = Element(Kacheln, 109)
K_{0111} = Element(Kacheln, 121)
K_{0112} = Element(Kacheln, 133)
K_{0201} = Element(Kacheln, 2)
K_{0202} = Element(Kacheln, 14)
K_{0203} = Element(Kacheln, 26)
K_{0204} = Element(Kacheln, 38)
K_{0205} = Element(Kacheln, 50)
K_{0206} = Element(Kacheln, 62)
K_{0207} = Element(Kacheln, 74)
K_{0208} = Element(Kacheln, 86)
K_{0209} = Element(Kacheln, 98)
K_{0210} = Element(Kacheln, 110)
K_{0211} = Element(Kacheln, 122)
K_{0212} = Element(Kacheln, 134)
K_{0301} = Element(Kacheln, 3)
K_{0302} = Element(Kacheln, 15)
K_{0303} = Element(Kacheln, 27)
K_{0304} = Element(Kacheln, 39)
K_{0305} = Element(Kacheln, 51)
K_{0306} = Element(Kacheln, 63)
K_{0307} = Element(Kacheln, 75)
K_{0308} = Element(Kacheln, 87)
K_{0309} = Element(Kacheln, 99)
K_{0310} = Element(Kacheln, 111)
K_{0311} = Element(Kacheln, 123)
K_{0312} = Element(Kacheln, 135)
K_{0401} = Element(Kacheln, 4)
K_{0402} = Element(Kacheln, 16)
K_{0403} = Element(Kacheln, 28)
K_{0404} = Element(Kacheln, 40)
K_{0405} = Element(Kacheln, 52)
K_{0406} = Element(Kacheln, 64)
K_{0407} = Element(Kacheln, 76)
K_{0408} = Element(Kacheln, 88)
K_{0409} = Element(Kacheln, 100)
K_{0410} = Element(Kacheln, 112)
K_{0411} = Element(Kacheln, 124)
K_{0412} = Element(Kacheln, 136)
K_{0501} = Element(Kacheln, 5)
K_{0502} = Element(Kacheln, 17)
K_{0503} = Element(Kacheln, 29)
K_{0504} = Element(Kacheln, 41)
K_{0505} = Element(Kacheln, 53)
K_{0506} = Element(Kacheln, 65)
K_{0507} = Element(Kacheln, 77)
K_{0508} = Element(Kacheln, 89)
K_{0509} = Element(Kacheln, 101)
K_{0510} = Element(Kacheln, 113)
K_{0511} = Element(Kacheln, 125)
K_{0512} = Element(Kacheln, 137)
K_{0601} = Element(Kacheln, 6)
K_{0602} = Element(Kacheln, 18)
K_{0603} = Element(Kacheln, 30)
K_{0604} = Element(Kacheln, 42)
K_{0605} = Element(Kacheln, 54)
K_{0606} = Element(Kacheln, 66)
K_{0607} = Element(Kacheln, 78)
K_{0608} = Element(Kacheln, 90)
K_{0609} = Element(Kacheln, 102)
K_{0610} = Element(Kacheln, 114)
K_{0611} = Element(Kacheln, 126)
K_{0612} = Element(Kacheln, 138)
K_{0701} = Element(Kacheln, 7)
K_{0702} = Element(Kacheln, 19)
K_{0703} = Element(Kacheln, 31)
K_{0704} = Element(Kacheln, 43)
K_{0705} = Element(Kacheln, 55)
K_{0706} = Element(Kacheln, 67)
K_{0707} = Element(Kacheln, 79)
K_{0708} = Element(Kacheln, 91)
K_{0709} = Element(Kacheln, 103)
K_{0710} = Element(Kacheln, 115)
K_{0711} = Element(Kacheln, 127)
K_{0712} = Element(Kacheln, 139)
K_{0801} = Element(Kacheln, 8)
K_{0802} = Element(Kacheln, 20)
K_{0803} = Element(Kacheln, 32)
K_{0804} = Element(Kacheln, 44)
K_{0805} = Element(Kacheln, 56)
K_{0806} = Element(Kacheln, 68)
K_{0807} = Element(Kacheln, 80)
K_{0808} = Element(Kacheln, 92)
K_{0809} = Element(Kacheln, 104)
K_{0810} = Element(Kacheln, 116)
K_{0811} = Element(Kacheln, 128)
K_{0812} = Element(Kacheln, 140)
K_{0901} = Element(Kacheln, 9)
K_{0902} = Element(Kacheln, 21)
K_{0903} = Element(Kacheln, 33)
K_{0904} = Element(Kacheln, 45)
K_{0905} = Element(Kacheln, 57)
K_{0906} = Element(Kacheln, 69)
K_{0907} = Element(Kacheln, 81)
K_{0908} = Element(Kacheln, 93)
K_{0909} = Element(Kacheln, 105)
K_{0910} = Element(Kacheln, 117)
K_{0911} = Element(Kacheln, 129)
K_{0912} = Element(Kacheln, 141)
K_{1001} = Element(Kacheln, 10)
K_{1002} = Element(Kacheln, 22)
K_{1003} = Element(Kacheln, 34)
K_{1004} = Element(Kacheln, 46)
K_{1005} = Element(Kacheln, 58)
K_{1006} = Element(Kacheln, 70)
K_{1007} = Element(Kacheln, 82)
K_{1008} = Element(Kacheln, 94)
K_{1009} = Element(Kacheln, 106)
K_{1010} = Element(Kacheln, 118)
K_{1011} = Element(Kacheln, 130)
K_{1012} = Element(Kacheln, 142)
K_{1101} = Element(Kacheln, 11)
K_{1102} = Element(Kacheln, 23)
K_{1103} = Element(Kacheln, 35)
K_{1104} = Element(Kacheln, 47)
K_{1105} = Element(Kacheln, 59)
K_{1106} = Element(Kacheln, 71)
K_{1107} = Element(Kacheln, 83)
K_{1108} = Element(Kacheln, 95)
K_{1109} = Element(Kacheln, 107)
K_{1110} = Element(Kacheln, 119)
K_{1111} = Element(Kacheln, 131)
K_{1112} = Element(Kacheln, 143)
K_{1201} = Element(Kacheln, 12)
K_{1202} = Element(Kacheln, 24)
K_{1203} = Element(Kacheln, 36)
K_{1204} = Element(Kacheln, 48)
K_{1205} = Element(Kacheln, 60)
K_{1206} = Element(Kacheln, 72)
K_{1207} = Element(Kacheln, 84)
K_{1208} = Element(Kacheln, 96)
K_{1209} = Element(Kacheln, 108)
K_{1210} = Element(Kacheln, 120)
K_{1211} = Element(Kacheln, 132)
K_{1212} = Element(Kacheln, 144)