14 lines
643 B
TeX
14 lines
643 B
TeX
\section{Isometries}
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\begin{remark}
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It is convenient to begin our discussion with the definition of an isometry (from the Greek \textit{isometros}, meaning "equal measure") in $\R^n$.
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\end{remark}
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\begin{definition}[Isometry]
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An \textit{isometry} of $n$-dimensional space $\R^n$ is a function from $\R^n$ onto $\R^n$ that preserves distance.
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\end{definition}
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\begin{definition}[Symmetry Group of a Figure in $\mathbf{\R^n}$]
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Let $F$ be a set of points in $\R^n$. the \textit{symmetry group of $F$} in $\R^n$ is the set of all isometries of $\R^n$ that carry $F$ onto itself. The group operation is function composition.
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\end{definition}
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