Circle of Curvature

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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.

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

\(f(x)=\sin(x)\)

\(f(x)=\)ln\((x)\)

\(f(x)=\cos(3x)e^{x/3}\)

\(f(x)=2\sin(x)+2\cos(3x)\)

\(f(x)=\sin(2x)+\)ln\((x+2)\)

\(f(x)=3x+\frac{1}{5x}-x^2+1\)

\(f(x)=\frac{\sin(4x)}{x}\)

\(f(x)=\)ln\((x)\cos(3x)\)

\(f(x)=\)ln\((x+2)+\sin(2x)-e^{-x}\)

x = 3

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