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Mathematik-Online lexicon:

Symmetry to a Point or to a Line

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Example 1:

Is there a symmetry to the line $ x=2$?

$\displaystyle f(x)=\frac{1}{4}x^4-2x^3+4x^2 $

One can verify that $ f(2+x)=f(2-x)$.

\includegraphics{symm1}

Example 2:

Is there a symmetry to the point $ P(1/-4)$?

$\displaystyle f(x)=x^3-3x^2-2 $

One can verify that $ f(1+x)-f(1)=-f(1-x)+f(1)$.

\includegraphics{symm2}

(Authors: Jahn/Knödler)

see also:

  automatisch erstellt am 29. 11. 2004