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Mathematics LibreTexts

Circle of Curvature

\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } 

\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}

\newcommand{\id}{\mathrm{id}} \newcommand{\Span}{\mathrm{span}}

( \newcommand{\kernel}{\mathrm{null}\,}\) \newcommand{\range}{\mathrm{range}\,}

\newcommand{\RealPart}{\mathrm{Re}} \newcommand{\ImaginaryPart}{\mathrm{Im}}

\newcommand{\Argument}{\mathrm{Arg}} \newcommand{\norm}[1]{\| #1 \|}

\newcommand{\inner}[2]{\langle #1, #2 \rangle}

\newcommand{\Span}{\mathrm{span}}

\newcommand{\id}{\mathrm{id}}

\newcommand{\Span}{\mathrm{span}}

\newcommand{\kernel}{\mathrm{null}\,}

\newcommand{\range}{\mathrm{range}\,}

\newcommand{\RealPart}{\mathrm{Re}}

\newcommand{\ImaginaryPart}{\mathrm{Im}}

\newcommand{\Argument}{\mathrm{Arg}}

\newcommand{\norm}[1]{\| #1 \|}

\newcommand{\inner}[2]{\langle #1, #2 \rangle}

\newcommand{\Span}{\mathrm{span}} \newcommand{\AA}{\unicode[.8,0]{x212B}}

\newcommand{\vectorA}[1]{\vec{#1}}      % arrow

\newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow

\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } 

\newcommand{\vectorC}[1]{\textbf{#1}} 

\newcommand{\vectorD}[1]{\overrightarrow{#1}} 

\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} 

\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}

\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } 

\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}

\newcommand{\avec}{\mathbf a} \newcommand{\bvec}{\mathbf b} \newcommand{\cvec}{\mathbf c} \newcommand{\dvec}{\mathbf d} \newcommand{\dtil}{\widetilde{\mathbf d}} \newcommand{\evec}{\mathbf e} \newcommand{\fvec}{\mathbf f} \newcommand{\nvec}{\mathbf n} \newcommand{\pvec}{\mathbf p} \newcommand{\qvec}{\mathbf q} \newcommand{\svec}{\mathbf s} \newcommand{\tvec}{\mathbf t} \newcommand{\uvec}{\mathbf u} \newcommand{\vvec}{\mathbf v} \newcommand{\wvec}{\mathbf w} \newcommand{\xvec}{\mathbf x} \newcommand{\yvec}{\mathbf y} \newcommand{\zvec}{\mathbf z} \newcommand{\rvec}{\mathbf r} \newcommand{\mvec}{\mathbf m} \newcommand{\zerovec}{\mathbf 0} \newcommand{\onevec}{\mathbf 1} \newcommand{\real}{\mathbb R} \newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]} \newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]} \newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]} \newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]} \newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]} \newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]} \newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]} \newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]} \newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]} \newcommand{\laspan}[1]{\text{Span}\{#1\}} \newcommand{\bcal}{\cal B} \newcommand{\ccal}{\cal C} \newcommand{\scal}{\cal S} \newcommand{\wcal}{\cal W} \newcommand{\ecal}{\cal E} \newcommand{\coords}[2]{\left\{#1\right\}_{#2}} \newcommand{\gray}[1]{\color{gray}{#1}} \newcommand{\lgray}[1]{\color{lightgray}{#1}} \newcommand{\rank}{\operatorname{rank}} \newcommand{\row}{\text{Row}} \newcommand{\col}{\text{Col}} \renewcommand{\row}{\text{Row}} \newcommand{\nul}{\text{Nul}} \newcommand{\var}{\text{Var}} \newcommand{\corr}{\text{corr}} \newcommand{\len}[1]{\left|#1\right|} \newcommand{\bbar}{\overline{\bvec}} \newcommand{\bhat}{\widehat{\bvec}} \newcommand{\bperp}{\bvec^\perp} \newcommand{\xhat}{\widehat{\xvec}} \newcommand{\vhat}{\widehat{\vvec}} \newcommand{\uhat}{\widehat{\uvec}} \newcommand{\what}{\widehat{\wvec}} \newcommand{\Sighat}{\widehat{\Sigma}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9}

View the Circle of Curvature

Below you can see the graph of a function, its curvature (\kappa),  its radius of curvature (r),  and its circle of curvature.  You can move the slider to see how the circle of curvature changes as you move along the curve.  Click "Next" to see a new curve.

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

x = 3

 


This page titled Circle of Curvature is shared under a not declared license and was authored, remixed, and/or curated by Larry Green.

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