Plot-Befehle in Mathematica am Beispiel der Ellipse

Plot der Kurve in Parameterform

In[4]:=

a = 3 ; b = 2 ;

In[1]:=

c[t_] := {a Cos[t], b Sin[t]}

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ParametricPlot[c[t], {t, -π, π}, AspectRatioAutomatic, AxesFalse, Epilog {Line[{{-a, 0}, {a, 0}}], Line[{{0, -b}, {0, b}}]}]

[Graphics:HTMLFiles/plot-curve_4.gif]

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⁃Graphics⁃

Plot der Kurve in Polarkoordinaten

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e := Sqrt[a^2 - b^2] ϵ := e/a r[ϕ_] := 1/(1 + ϵ Cos[ϕ])

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<<Graphics`Graphics`

In[19]:=

PolarPlot[r[ϕ], {ϕ, -π, π}, AspectRatioAutomatic, TicksFalse]

[Graphics:HTMLFiles/plot-curve_9.gif]

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⁃Graphics⁃

Plot der implizit gegebenen Kurve

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<<Graphics`ImplicitPlot`

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F[x_, y_] := (x/a)^2 + (y/b)^2

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ImplicitPlot[ F[x, y] 1, {x, -a, a}, {y, -b, b}, AxesFalse, AspectRatioAutomatic, Epilog {Line[{{-a, 0}, {a, 0}}], Line[{{0, -b}, {0, b}}]}]

[Graphics:HTMLFiles/plot-curve_14.gif]

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⁃ContourGraphics⁃

Plot der explizit gegeben Kurve

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Clear[a, b]

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sol = Solve[F[x, y] 1, {y}]

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{{y -(b^2 - (b^2 x^2)/a^2)^(1/2)}, {y (b^2 - (b^2 x^2)/a^2)^(1/2)}}

In[50]:=

f1 = Function[x, y/.sol[[1]]] f2 = Function[x, y/.sol[[2]]]

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Function[x, y/.sol〚1〛]

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Function[x, y/.sol〚2〛]

In[52]:=

f1[x]

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-(b^2 - (b^2 x^2)/a^2)^(1/2)

In[53]:=

a = 3 ; b = 2 ; Plot[f1[x], {x, -a, a}, AspectRatioAutomatic, TicksNone]

[Graphics:HTMLFiles/plot-curve_25.gif]

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⁃Graphics⁃

In[55]:=

Plot[{f1[x], f2[x]}, {x, -a, a}, AspectRatioAutomatic, TicksNone]

[Graphics:HTMLFiles/plot-curve_28.gif]

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⁃Graphics⁃

Created by Mathematica  (April 5, 2005)